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

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 ( =) 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 =) 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)
• 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)