A Study to Evaluate the Efficacy and Safety of Daratumumab in Pediatric and Young Adult Participants Greater Than or Equal to (>=)1 and Less Than or Equal to (<=) 30 Years of Age With Relapsed/Refractory Precursor B-cell or T-cell Acute Lymphoblastic Leukemia or Lymphoblastic Lymphoma

Screening for eligible participants will be performed within 21 days before administration of the study drug. Participants with B-cell ALL/LL will receive treatment until disease progression, unacceptable toxicity or achievement of CR followed by hematopoietic stem cell transplant (HSCT). Participants with T cell ALL/LL will receive treatment for up to 2 cycles. If disease progression is confirmed, then the participant will discontinue study treatment, complete the End of Treatment Visit, and enter the Posttreatment Period. For those participants who discontinue study drug prior to disease progression, disease evaluations will continue to be performed every 8 weeks until subsequent anticancer therapy is initiated.

Inclusion criteria

• Documented acute lymphoblastic leukemia (ALL) or lymphoblastic lymphoma (LL) as defined by the criteria below:

• B-cell cohort: Stage 1; ALL in second or greater relapse or refractory to 2 prior induction regimens with greater than or equal to (>=) 5 percent (%) blasts in the bone marrow and aged 1 to less than (<) 18 years. Stage 2; ALL in second or greater relapse or refractory to 2 prior induction regimens with (>=) 5% blasts in the bone marrow and aged 1 to 30 years. LL in second or greater relapse or refractory to 2 prior induction regimens and biopsy proven and with evidence of measurable disease by radiologic criteria and aged 1 to 30 years.
• T-cell cohort: Stage 1; ALL in first relapse or refractory to 1 prior induction/consolidation regimen with (>=) 5% blasts in the bone marrow and aged 1 to <18 years. Stage 2; ALL in first relapse or refractory to 1 prior induction/consolidation regimen with (>=) 5% blasts in the bone marrow and aged 1 to 30 years. LL in first relapse or refractory to 1 prior induction/consolidation regimen biopsy proven and with evidence of measurable disease by radiologic criteria and aged 1 to 30 years
• Performance status greater than or equal to (>=) 70 by Lansky scale (for participants less than [<] 16 years of age) or Karnofsky scale (for participants [>=] 16 years of age)
• Adequate hematology laboratory values at Cycle 1 Day 1 pre-dosing defined as follows:

• Hemoglobin (>=) 7.5 gram per deciliter (g/dL) ([>=] 5 millimole per liter [mmol/L]; prior red blood cell [RBC] transfusion is permitted)
• Platelet count (>=) 10*10^9 per liter (L) (prior platelet transfusion is permitted)
• Adequate renal function defined as normal serum creatinine for the participant's age or creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70 milliliter per minute per 1.73 square meter (mL/min/1.73 m^2) prior to enrollment
• Adequate liver function prior to enrollment defined as:

• Alanine aminotransferase level less than or equal to (<=) 2.5* the upper limit of normal (ULN),
• Aspartate aminotransferase level (<=) 2.5* ULN, and
• Total bilirubin (<=) 2* ULN or direct bilirubin level (<=) 2.0* ULN

Exclusion criteria

• Received an allogeneic hematopoietic transplant within 3 months of screening
• Active acute graft-versus-host disease of any grade or chronic graft-versus-host disease of Grade 2 or higher
• Received immunosuppression post hematopoietic transplant within 1 month of study entry
• Philadelphia chromosome positive (Ph+) B-cell ALL eligible for tyrosine kinase inhibitor therapy
• Has either of the following:

• Evidence of dyspnea at rest or oxygen saturation (<=) 94 percent (%).
• Known moderate or severe persistent asthma within the past 2 years, or uncontrolled asthma of any classification
• Received an investigational drug, was vaccinated with live attenuated vaccines, or used an invasive investigational medical device within 4 weeks before the planned first dose of study drug, or is currently being treated in an investigational study
• Known to be seropositive for human immunodeficiency virus (HIV)
• Any one of the following:

• Seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen [HBsAg]). Participants with resolved infection (ie, participants who are HBsAg negative but positive for antibodies to hepatitis B core antigen [anti-HBc] and/or antibodies to hepatitis B surface antigen [anti-HBs]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) deoxyribonucleic acid (DNA) levels. Those who are PCR positive will be excluded
• Known to be seropositive for hepatitis C (except in the setting of a sustained virologic response [SVR], defined as aviremia at least 12 weeks after completion of antiviral therapy)