Inclusion Criteria:

- STEP 1:

- Cytologically or histologically confirmed non-small cell lung carcinoma (NSCLC)

- Predominant non-squamous histology (patients with NSCLC not otherwise specified [NOS]
are eligible); mixed tumors will be categorized by the predominant cell type; if
small cell elements are present the patient is ineligible

- Stage IV disease (includes M1a, M1b, or recurrent disease), according to the 7th
edition of the lung cancer TNM classification system

- Epidermal growth factor receptor (EGFR) mutation testing of tumor must have
previously been performed and not demonstrate an EGFR tyrosine kinase inhibitor
sensitizing mutation (at minimum, testing for EGFR Exon 19 deletion or Exon 21 L858R
mutations must have been included); Patients in whom EGFR mutation testing has been
attempted and is inconclusive (for example, due to lack of sufficient DNA yield), or
patients with a known alternative driver mutation (for example, KRAS mutation) but
unknown EGFR mutation status may be enrolled provided that tissue exists for MET
immunohistochemical testing

- Patients must have measurable disease as defined by Response Evaluation Criteria in
Solid Tumors (RECIST) v 1.1 criteria; baseline measurements and evaluation of ALL
sites of disease must be obtained within 4 weeks prior to registration

- Prior to registration, the investigator/site must confirm that sufficient pathology
material representative of patient's cancer is available for submission for MET
immunohistochemical testing; patients for whom there is not sufficient pathology
material representative of the patient's cancer (tumor block or 10 unstained slides)
are not eligible to participate in this study

- Patients must have received one or two lines of prior chemotherapy (first line
platinum-doublet based chemotherapy plus switch maintenance chemotherapy counts as
one line of therapy); prior adjuvant chemotherapy for early stage disease does not
count as one line of therapy if 12 months or greater elapsed between completion of
adjuvant therapy and initiation of first-line systemic therapy; if less than 12
months elapsed, adjuvant chemotherapy counts as one line of therapy

- No prior erlotinib, other EGFR tyrosine kinase inhibitor therapy, vascular
endothelial growth factor (VEGRF) tyrosine kinase inhibitor therapy, Met tyrosine
kinase inhibitor therapy, or Met monoclonal antibody (MetMAb); prior antibody therapy
such as bevacizumab or cetuximab is allowed with a washout period depending on dosing
interval and investigational nature

- Any prior chemotherapy (based on administration schedule) must have been completed in
greater than or equal to the following times prior to registration:

- Chemotherapy administered in a daily schedule must be completed >= 2 weeks prior
to registration

- Chemotherapy administered in a weekly schedule must be completed >= 2 weeks
prior to registration

- Chemotherapy administered in a 2-weekly schedule must be completed >= 3 weeks
prior to registration

- Chemotherapy administered in a 3-weekly schedule must be completed >= 4 weeks
prior to registration

- Patients must have discontinued treatment with any other type of investigational
agent >= 4 weeks prior to registration

- Patients must have recovered to baseline or Common Terminology Criteria for Adverse
Events (CTCAE) =< grade 1 from toxicity due to all prior therapies except alopecia
and other non-clinically significant adverse events (AEs)

- Patients with no known brain metastasis at baseline must have baseline brain imaging
within 12 weeks prior to study registration not demonstrating brain metastases;
patients with brain metastases at baseline must have baseline brain imagining within
4 weeks prior to study registration and meet all of the following criteria:

- Have completed treatment to all active brain metastases (with whole brain
radiation or radiosurgery) >= 2 weeks prior to registration, or have undergone
complete neurosurgical resection >= 3 months prior to registration;

- Be asymptomatic from brain metastases at time of screening;

- Not require steroid treatment or enzyme inducing anticonvulsant drugs for at
least 2 weeks prior to registration; non-enzyme inducing anti-epileptic drugs
(NEIAED) such as levetiracetam are allowed;

- Known leptomeningeal disease or epidural disease is not allowed

- Patients must not have received radiation therapy to the thoracic cavity, abdomen, or
pelvis within 3 months prior to registration, to bone or brain metastasis within 14
days prior to registration, or to any other site within 28 days prior to registration

- Radiation related toxicities must have resolved to =< grade 1 prior to registration

- Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status
between 0-2

- Patients must have an anticipated life expectancy greater than 3 months

- Leukocytes >= 3,000/mm^3

- Absolute neutrophil count >= 1,500/ mm^3

- Platelets >= 100,000/mm^3

- Hemoglobin >= 9 g/dL

- Total bilirubin =< 1.5 institutional upper limit of normal (ULN)

- Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase [SGPT]) =< 3 x
ULN

- Serum albumin >= 2.8g/dL

- Lipase =< 2.0 x ULN and no radiologic or clinical evidence of pancreatitis

- Serum phosphorus >= institutional lower limit of normal (LLN)

- Serum calcium >= LLN

- Serum magnesium >= LLN

- Serum potassium >= LLN

- Creatinine =<1.5 x ULN or calculated or measured creatinine clearance >= 50
mL/min/1.73m^2 (normalized to body surface area [BSA]) for patients with creatinine
levels above institutional normal

- Screening urine dipstick must equal 0 or "trace"; if urine dipstick results are >=
1+, calculation of urine protein creatinine (UPC) is required and patients must have
a UPC ratio =< 1 to participate in the study

- Prothrombin time (PT)/ international normalized ratio (INR) and partial
thromboplastin time (PTT) test =< 1.3 x ULN

- No history of the following:

- Clinically-significant gastrointestinal bleeding within 6 months prior to
registration

- Hemoptysis of >= 0.5 teaspoon (2.5 mL) of red blood within 3 months prior to
registration

- Any other signs indicative of pulmonary hemorrhage within 3 months prior to
registration

- No radiographic or other evidence of:

- Tumor invading the gastrointestinal (GI) tract (esophagus, stomach, small or
large bowel, rectum or anus), or any evidence of endotracheal or endobronchial
tumor within 28 days prior to registration

- Cavitating pulmonary lesion(s)

- Tumor in contact with, invading or encasing any major blood vessels

- No patients with psychiatric illness/social situations that would limit compliance
with study requirements

- No history of major thrombotic events (deep vein thrombosis [DVT] or pulmonary
embolism [PE]) within 6 months prior to registration; Note: subjects with a venous
filter (e.g. vena cava filter) are not eligible for this study

- No concomitant treatment, in therapeutic doses, with anticoagulants such as Warfarin
or Warfarin-related agents, heparin, low molecular weight heparin (LMWH), thrombin or
Factor Xa inhibitors, or antiplatelet agents (e.g., clopidogrel [clopidogrel
bisulfate]); (low dose aspirin [=< 81 mg/day] and prophylactic LMWH are permitted)

- No concomitant treatment of strong cytochrome P450 3A4 (CYP3A4) inducers (e.g.,
dexamethasone, phenytoin, carbamazepine, rifampin, rifabutin, rifapentine,
phenobarbital, and St. John's wort)

- No cardiovascular disorders including:

- Congestive heart failure (CHF): New York Heart Association (NYHA) class III
(moderate) or class IV (severe) at the time of screening

- Concurrent uncontrolled hypertension defined as sustained blood pressure (BP) >
150 mm Hg systolic, or > 100 mm Hg diastolic despite optimal antihypertensive
treatment within 7 days prior to registration

- Any history of congenital long QT syndrome

- Any of the following within 6 months prior to registration:

- Unstable angina pectoris

- Clinically-significant cardiac arrhythmias

- Stroke (including transient ischemic attack [TIA], or other ischemic event)

- Myocardial infarction

- No gastrointestinal disorders particularly those associated with a high risk of
perforation or fistula formation including:

- Any of the following within 28 days prior to registration

- Intra-abdominal tumor/metastases invading GI mucosa

- Active peptic ulcer disease

- Inflammatory bowel disease (including ulcerative colitis and Crohn's
disease), diverticulitis, cholecystitis, symptomatic cholangitis or
appendicitis

- Malabsorption syndrome

- Any of the following within 6 months prior to registration:

- Abdominal fistula

- Gastrointestinal perforation

- Bowel obstruction or gastric outlet obstruction

- Intra-abdominal abscess; Note: complete resolution of an intra-abdominal
abscess must be confirmed prior to initiating treatment with cabozantinib
even if the abscess occurred more that 6 months prior to registration

- No other disorders associated with a high risk of fistula formation including
percutaneous endoscopic gastrostomy (PEG) tube placement within 3 months prior to
registration

- No uncontrolled, significant, intercurrent or recent illness including, but not
limited to, the following conditions:

- Active infection requiring systemic treatment within 28 days prior to
registration

- Serious non-healing wound/ulcer/bone fracture within 28 days prior to
registration

- History of organ transplant

- Concurrent uncompensated hypothyroidism or thyroid dysfunction within 7 days
prior to registration

- History of surgery as follows:

- Major surgery (as an example, surgery requiring anesthesia and a > 24 hour
hospital stay) within 3 months prior to registration if there were no wound
healing complications or within 6 months prior to registration if there
were wound complications

- Minor surgery (such as chest tube placement, but not including
thoracentesis or paracentesis) within 28 days prior to registration if
there were no wound healing complications or within 3 months prior to
registration if there were wound complications

- In addition, complete wound healing from prior surgery and procedures must
be confirmed prior to registration

- Patients must have corrected QT interval calculated by the Fridericia formula (QTcF)
=< 500 ms within 28 days before registration

- Patients must be able to swallow tablets

- No prior malignancy within 2 years prior to registration which required systemic
treatment or is currently active

- Women must not be pregnant or breast-feeding; for this reason, all females of
childbearing potential must have a blood test or urine study within 2 weeks prior to
registration to rule out pregnancy; a female of childbearing potential is any woman,
regardless of sexual orientation or whether they have undergone tubal ligation, who
meets the following criteria: 1) has not undergone a hysterectomy or bilateral
oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive
months (i.e., has had menses at any time in the preceding 24 consecutive months)

- Sexually active subjects (men and women) must agree to use medically accepted
barrier methods of contraception (e.g. male or female condom) during the course
of the study and for 4 months after the last dose of study drug(s), even if oral
contraceptives are also used; all sexually active subjects of reproduction
potential must agree to use both a barrier method and a second method of birth
control during the course of the study and for 4 months after the last dose of
study drug(s)

- Patients with known human immunodeficiency virus (HIV) disease taking antiretroviral
therapy are excluded

- STEP 2: Patients must have radiographic progressive disease per RECIST criteria after
>= 2 courses of therapy on Arm A or Arm B

- STEP 2: Patients may not have central nervous system progression but patients with
stable central nervous system (CNS) disease are allowed

- STEP 2: Patients must be registered to Step 2 within 4 weeks of the last dose of
treatment administration from Step 1

- STEP 2: Patients must have an ECOG performance status between 0-2

- STEP 2: Patients must have recovered to baseline (pre-Step 1) or CTCAE =< grade 1
from toxicity due to all prior therapies except alopecia and other non-clinically
significant AEs

- STEP 2: Leukocytes >= 3,000/mm^3

- STEP 2: Absolute neutrophil count >= 1,500/mm^3

- STEP 2: Platelets >= 100,000/mm^3

- STEP 2: Hemoglobin >= 9 g/dL

- STEP 2: Total bilirubin =< 1.5 x ULN

- STEP 2: AST(SGOT) and ALT(SGPT) =< 3 x ULN

- STEP 2: Serum albumin >= 2.8g/dL

- STEP 2: Lipase =< 2.0 x ULN and no radiologic or clinical evidence of pancreatitis

- STEP 2: Serum phosphorus >= LLN

- STEP 2: Serum calcium >= LLN

- STEP 2: Serum magnesium >= LLN

- STEP 2: Serum potassium >= LLN

- STEP 2: Creatinine =< 1.5 x ULN or calculated or measured creatinine clearance >= 50
mL/min/1.73m^2 (normalized to BSA) for patients with creatinine levels above
institutional normal

- STEP 2: Screening urine dipstick must equal 0; if urine dipstick results are >= 1+,
calculation of UPC is required and patients must have a UPC ration =< 1 to
participate in the study

- STEP 2: Patients must have corrected QT interval calculated by the Fridericia formula
(QTcF) =< 500 ms within 28 days before registration

- STEP 2: No intercurrent illness or disease complication that the investigator
believes would limit the ability to safely tolerate the combination of erlotinib and
cabozantinib