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:

  1. 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.
  2. 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:

  1. Hemoglobin (\>=) 7.5 gram per deciliter (g/dL) (\[\>=\] 5 millimole per liter \[mmol/L\]; prior red blood cell \[RBC\] transfusion is permitted)
  2. 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:

  1. Alanine aminotransferase level less than or equal to (\<=) 2.5\* the upper limit of normal (ULN),
  2. Aspartate aminotransferase level (\<=) 2.5\* ULN, and
  3. 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:

  1. Evidence of dyspnea at rest or oxygen saturation (\<=) 94 percent (%).
  2. 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:

  1. 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
  2. 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)