Inclusion Criteria:

- Patients must have histologically or cytologically confirmed intermediate or high
grade B-cell Non-Hodgkin lymphoma with primary progressive or relapsed disease

- Patients may have had up to 4 prior chemo-and-or radiation therapy regiments,
including one autologous transplant based protocol; any prior therapy (chemotherapy
or radiation) must have been completed at least 4 weeks prior to start of this
protocol; for prior high-dose chemotherapy with stem cell transplant, a 6-week
interval is required; all side effects must have resolved

- Karnofsky performance status >= 60%

- Life expectancy of greater than 3 months

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

- Platelets >= 50,000 mm^3

- Total bilirubin =< 1.5 mg/dl

- Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) =<
2.5 x institutional upper limit of normal

- Creatinine within normal institutional limits OR creatinine clearance >= 50 mL/min
for creatinine levels above institutional normal (calculated or measured)

- Cardiac ejection fraction of > 40% by echocardiogram or multi gated acquisition
(MUGA) scan

- Have no serious or intercurrent medical illness

- Voluntary written informed consent before performance of any study-related procedure
not part of normal medical care, with the understanding that consent may be withdrawn
by the subject at any time without prejudice to future medical care

- Female subject is either post-menopausal or surgically sterilized or willing to use
an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine
device, diaphragm with spermicide, condom with spermicide, or abstinence) for the
duration of the study

- Male subject agrees to use an acceptable method for contraception for the duration of
the study

Exclusion Criteria:

- Patient has a platelet count of < 20 x 10^9/L with 7 days before enrollment

- Patient has an absolute neutrophil count of < 1.0 x 10^9/L within 7 days before
enrollment

- Patient has a calculated or measured creatinine clearance of < 30 ml/min with 14 days
before enrollment

- Patient has >= Grade 2 peripheral neuropathy within 14 days before enrollment

- Patient has hypersensitivity to bortezomib, boron, or mannitol

- Female subject is pregnant or breastfeeding; confirmation that the subject is not
pregnant must be established by a negative serum beta-human chorionic gonadotropin
(beta-hCG) pregnancy test result obtained during screening; pregnancy testing is not
required for postmenopausal or surgically sterilized women

- Patient has received other investigational drugs with 14 days before enrollment

- Serious medical or psychiatric illness likely to interfere with participation in this
clinical study

- Patients who have had more than 4 prior different chemotherapy regimens will be
excluded; patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks
for autologous transplant regimens) prior to entering the study or those who have not
recovered from adverse events due to agents administered more than 4 weeks earlier

- Patients may not have previously received VELCADE or gemcitabine

- Patients with active central nervous system (CNS) involvement are not eligible

- Human immunodeficiency virus (HIV)-positive patients receiving combination
anti-retroviral therapy

- Uncontrolled intercurrent illness including, but not limited to, ongoing or active
infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
arrhythmia, or psychiatric illness/social situations that would limit compliance with
study requirements