CAT-8015 in Children, Adolescents and Young Adults With Acute Lymphoblastic Leukemia or Non-Hodgkin's Lymphoma

Inclusion Criteria:

\- Histologically confirmed diagnosis of acute lymphoblastic leukemia (ALL) or non-Hodgkin's lymphoma (NHL) including lymphoblastic lymphoma, Burkitt's lymphoma, and large cell lymphoma; - Measurable or evaluable disease. - Evidence of CD22-positive malignancy by one of the following criteria: - greater than or equal to (\>=) 30 % of malignant cells from a disease site cluster of differentiation 22+ (CD22+) by fluorescence-activated cell sorter (FACS) analysis or; ≥ 15 % of malignant cells from a disease site CD22+ by immunohistochemistry (IHC). Stage of disease: - Participants must have relapsed or refractory disease and have received at least one standard chemotherapy and one salvage regimen or allogeneic stem cell transplant; - Relapse after prior autologous or allogeneic HSCT is allowed. In the event of relapse after prior allogeneic HSCT, the participant must be at least 100 days post-transplant and have no evidence of ongoing active graft-vs-host disease; - Recovered from the acute toxic effects of all prior therapy before entry. Performance status: - Participants greater than or equal to (\>=) 12 years of age: Eastern Cooperative Oncology Group (ECOG) score of 0, 1, 2, or 3; - Participants \< 12 years of age: Lansky scale \>= 50%; - Participants who are unable to walk because of paralysis, but who are up in a wheel chair will be considered ambulatory for the purpose of calculating the performance score. Participants with the following central nervous system (CNS) status, are eligible only in the absence of neurologic symptoms suggestive of CNS leukemia, such as cranial nerve palsy. - Female and male participants with childbearing potential and their sexual partners must agree to use an approved method of contraception during the study.

Exclusion Criteria:

\- Participants meeting any of the following criteria are not eligible for participation in the study: - Isolated testicular or CNS ALL; Hepatic function: - Inadequate liver function defined as total bilirubin \> 2 × upper limit of normal (ULN) (except in the case of participants with documented Gilbert's disease \> 5 × ULN) or transaminases (ALT and aspartate aminotransferase \[AST\]) \> 5 × ULN based on age- and laboratory-specific normal ranges; Renal function: - With greater than age-adjusted normal serum creatinine (see Table below) and a creatinine clearance \> 60 millilitre per minute mL/min/1.73 m2. - Age(Years)- Maximum Serum Creatinine (mg/dl)\[≤5,0.8\] \[5 \< age less than or equal to 10,1.0\] \[10 \< age less than or equal to 15,1.2 \[\> 15, 1.5\] Hematologic function: - For non-leukemic subjects only, absolute neutrophil count (ANC) \< 1000/cmm, or platelet count \< 50,000/cmm, if these cytopenias are not judged by the investigator to be due to underlying disease (ie potentially reversible with anti-neoplastic therapy); - Participants with CNS 3 disease; - Hyperleukocytosis (≥ 50,000 blasts/µL) or rapidly progressive disease (PD) that in the estimation of the investigator and sponsor would compromise ability to complete study therapy; - Prior treatment with CAT-3888 (BL22) or any pseudomonas-exotoxin-containing compound; - HIV positive serology (due to increased risk of severe infection and unknown interaction of CAT-8015 with antiretroviral drugs); - Active hepatitis B or C infection.