An Efficacy and Safety Proof of Concept Study of Daratumumab in Relapsed/Refractory Mantle Cell Lymphoma, Diffuse Large B-Cell Lymphoma, and Follicular Lymphoma

Inclusion Criteria: * Has diagnosis and prior treatment for each non-hodgkin's lymphoma (NHL) subtype as defined below: Mantle cell lymphoma (MCL): pathologically verified diagnosis of MCL based on local pathology report, relapsed or refractory disease after at least 2 prior lines of therapy, including at least 1 cycle of Bruton's tyrosine kinase (BTK) inhibitor therapy and documented progressive disease (PD) during or after BTK inhibitor treatment or participants who could not tolerate BTK inhibitor \[ie, discontinued BTK inhibitor due to adverse events (AEs)\], b) Diffuse large B cell lymphoma (DLBCL): pathologically confirmed diagnosis of non-transformed DLBCL, and relapsed or refractory disease; for those participants who have not received HDT/ASCT are not eligible for HDT/ASCT due to comorbidities, c) Follicular lymphoma (FL): pathologically confirmed diagnosis of FL of Grade 1, 2, or 3a according to World Health Organization (WHO) criteria without pathological evidence of transformation, and relapsed disease after at least two prior systemic therapies including one anti-CD20 containing combination regimen * At least 1 measurable site of disease * Participants must have available archival or fresh tumor tissue or both to submit to a central laboratory for CD38 assay. Expression of CD38 is measured by immunohistochemistry on fresh or archived tumor sample by central assessment using a CD38 investigational IHC assay under development: a) Stage 1: participants whose tumors are more than or equal to (\>=) 50 percent (%) positive for CD38, b) Stage 2: participant has less than (\<) 50% CD38+ or greater than (\>) 50% CD38+ depending on the distribution of CD 38 expression of enrolled participants during Stage 2. The sponsor will advise on which eligibility criterion is permitted during the enrollment period * Participant must have an ECOG performance status score of 0 or 1 * Women of childbearing potential must be practicing a highly effective method of birth control consistent with local regulations regarding the use of birth control methods for participants participating in clinical studies: example, established use of oral, injected or implanted hormonal methods of contraception; placement of an intrauterine device (IUD) or intrauterine system (IUS); barrier methods: condom with spermicidal foam/gel/film/cream/suppository or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository; male partner sterilization (the vasectomized partner should be the sole partner for that participant); true abstinence (when this is in line with the preferred and usual lifestyle of the participant) during and after the study (3 months after the last dose of any component of the treatment regimen) * A woman of childbearing potential must have a negative serum or urine pregnancy test within 14 days before commencing treatment. Females of reproductive potential must commit either to abstain continuously from heterosexual sexual intercourse or to use 2 methods of reliable birth control simultaneously * A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control example, either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also not donate sperm during the study and for 3 months after receiving the last dose of any component of the treatment regimen. The exception to this restriction is that if the participant's female partner is surgically sterile, a second method of birth control is not required Exclusion Criteria: * Known central nervous system lymphoma * Prior anti-tumor therapy including (all times measured prior to start of study drug): nitrosoureas within 6 weeks, chemotherapy within 3 weeks, therapeutic antibodies within 4 weeks, radio- or toxin-immunoconjugates within 10 weeks, radiation therapy within 2 weeks, investigational agents within 3 weeks, unless antibody this should be within 4 weeks * Daratumumab or other anti-CD38 therapies * Participant has a history of malignancy (other than NHL) within 3 years before the screening period (exceptions are squamous and basal cell carcinomas of the skin and carcinoma in situ of the cervix, non-muscle invasive bladder cancer (papillary neoplasms of low malignant potential and primary non-invasive tumors), or malignancy that in the opinion of the investigator, with concurrence with the sponsor's medical monitor, is considered cured with minimal risk of recurrence within 2 years) * Participant has known chronic obstructive pulmonary disease (COPD) with a Forced Expiratory Volume in 1 second (FEV1) less than (\<) 50% predicted normal. Note that FEV1 testing is required for participants suspected of having COPD and participants must be excluded if FEV1 \<50% b) Participant has known moderate or severe persistent asthma within 2 years (see Attachment 4: NHLBI table of asthma severity), or currently has uncontrolled asthma of any classification. (Note that participants who currently have controlled intermittent asthma or controlled mild persistent asthma are allowed in the study)