Safety Study of CAT-8015 to Treat Advanced B-cell Non-Hodgkin Lymphoma and Chronic Lymphocytic Leukemia (NHL or CLL)

Inclusion Criteria:

* Written informed consent and Health Insurance Portability and Accountability Act (HIPAA) authorization
* Participants must have histologically confirmed B-cell CLL, including small lymphocytic lymphoma (SLL), DLBCL, MCL, or FL
* B-cell NHL: a) Have previous confirmation of B-cell NHL b) Participants with DLBCL or MCL, must have relapsed or refractory disease after at least one prior regimen containing rituximab, either alone or in combination, and be ineligible for any available standard line of therapy known to be life-prolonging or life-saving c) Participants with FL, must have relapsed or refractory disease after at least two prior regimens, one of which included rituximab, either alone or in combination, and be ineligible for any available standard line of therapy known to be life-prolonging or life-saving d) Have measurable disease (at least one lesion greater than or equal to (≥) 20 millimeter (mm) in one dimension or ≥ 15 mm in two dimensions as measured by conventional or high resolution \[spiral\] computed tomography e) Not be a candidate for a hematopoietic stem cell (HSC) or bone marrow transplant
* B-cell CLL: a) Have previous confirmation of B-cell CLL with a characteristic immunophenotype by flow cytometry b) Have relapsed or refractory disease after at least 2 prior lines of treatment, at least 1 of which must have contained rituximab and be ineligible for any available standard line of therapy known to be life-prolonging or life-saving c) Not be a candidate for an HSC or BM transplant d) Have symptomatic disease that requires treatment
* Karnofsky Performance Status ≥ 70
* Life expectancy of ≥ 12 weeks
* Toxicities from previous cancer therapies must have recovered to Grade less than (\<) 2
* Adequate hematological function defined as: a) Hemoglobin ≥ 9 g/dL b) Absolute neutrophil count ≥ 1500/mm\^3 c) Platelet count ≥ 75,000/mm\^3
* Prothrombin time-International Normalized Ratio/Partial thromboplastin time less than or equal to (≤) 1.5 × upper limit of normal (ULN), or for participants on anticoagulation therapy, status within therapeutic range
* Women of non-child-bearing potential or using effective contraception
* Male participants with partners of child-bearing potential must be surgically sterile or use a contraceptive method

Exclusion Criteria:

* Any available standard line of therapy known to be life-prolonging or life-saving
* Any concurrent chemotherapy, radiotherapy, immunotherapy, biologic, or hormonal therapy for treatment of cancer
* For CLL participants only, rapidly progressive disease that in the estimation of the investigator and sponsor would compromise ability to complete study therapy
* History of allergy or reaction to any component of the CAT-8015
* Receipt of any chemotherapy or small molecule targeted therapy or any biological- or immunological-based therapies for leukemia or lymphoma within 6 weeks
* Prior radiation therapy will not be excluded, providing the volume of bone marrow treated is less than 25 percent
* Any history of prior pseudomonas-exotoxin immunotoxin administration including CAT-8015, CAT-3888, or LMB-2
* History of other invasive malignancy within 5 years, with some exceptions
* Evidence of significant active infection requiring antimicrobial, antifungal, antiparasitic or antiviral therapy or for which other supportive care is given
* Autologous stem cell transplantation within 6 months prior to study entry
* Allogenic stem cell transplantation or any other organ transplant
* HIV-positive or AIDS, Hepatitis B or hepatitis C infection as defined by seropositive for hepatitis B (HBsAg) or hepatitis C and elevated liver transaminases
* Use of immunosuppressive medication other than steroids within 7 days, use of systemic steroids within 7 days before the first dose of CAT-8015 (inhaled and topical corticosteroids are permitted). Participants may take replacement doses of steroids (defined as ≤ 30 mg/day hydrocortisone or the equivalent) if on a stable dose for at least 2 weeks prior to the first dose of CAT-8015
* Documented current central nervous system involvement by leukemia or lymphoma
* Pregnancy or lactation, other severe, concurrent diseases
* Concurrent enrollment in another clinical study