Daratumumab, Bortezomib, Dexamethasone, Pegylated Liposomal Doxorubicin Hydrochloride, and Lenalidomide in Treating Participants With Plasma Cell Leukemia

Inclusion Criteria:

* Documented informed consent of the participant and/or legally authorized representative. Assent, when appropriate, will be obtained per institutional guidelines.
* Willingness to provide bone marrow and peripheral blood samples for research purposes. If unavailable, exceptions may be granted with study principal investigator (PI) approval.
* All study participants must be registered into the mandatory Revlimid Risk Evaluation and Mitigation Strategies (REMS) program and be willing to comply with its requirements.
* Karnofsky performance status (KPS) \> 60.
* Plasma cell leukemia; either newly diagnosed or relapsed: defined as the presence of \> 2 x 10\^9/L peripheral blood plasma cells or plasmacytosis accounting for \> 20% of the differential white cell count.
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Absolute neutrophil count (ANC) \>= 500/mm\^3

  * NOTE: Growth factor is not permitted within 14 days of ANC assessment unless cytopenia is secondary ot disease involvement.
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Total bilirubin =\< 2.0 x ULN (unless has Gilbert's disease).
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Aspartate aminotransferase (AST) =\< 3.0 x ULN.
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Alanine aminotransferase (ALT) =\< 3.0 x ULN.
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Creatinine clearance of \>= 30 mL/min per 24 hour urine test or the Cockcroft-Gault formula.
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Left ventricular ejection fraction (LVEF) \> 45%
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Hemoglobin \>= 8.0 g/dL

  * Note: Transfusion support is allowed.
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Seronegative for human immunodeficiency virus (HIV) antigen-antibody (Ag/Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative), and syphilis (RPR).

  * If positive, hepatitis C RNA quantitation must be performed.
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Meets other institutional and federal requirements for infectious disease titer requirements.

  * Note: Infectious disease testing to be performed within 28 days prior to day 1 of protocol therapy.
* Within 14 days prior to day 1 of protocol therapy unless otherwise stated: Women of childbearing potential (WOCBP): negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.
* Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy.

  * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only).
* Women of childbearing potential must follow pregnancy testing requirements as outline in REMS program material.

Exclusion Criteria:

* Progression or intolerance to daratumumab, bortezomib, or lenalidomide.
* Prior stem cell transplant.
* Participant is receiving concurrent chemotherapy or biologic or hormonal therapy for cancer treatment.

  * Note: Concurrent use of hormones for noncancer-related conditions (e.g., insulin for diabetes) is acceptable.
* Vaccination with live attenuated vaccines within 4 weeks of first study agent administration.
* Participant is currently using or has used immunosuppressive medication within 14 days prior to the first study dose of study treatment. The following are exceptions:

  * Intranasal, topical, inhaled, or local steroid injections (e.g., intra-articular injection)
  * Chronic systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or equivalent
  * Steroids as premedication for hypersensitivity reactions (e.g., infusion-related reactions, computed tomography \[CT\] scan premedication).
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent.
* Has known chronic obstructive pulmonary disease with a forced expiratory volume in 1 second (FEV1) \< 50% of predicted normal.
* Has known moderate or severe persistent asthma within the past 2 years, or currently has uncontrolled asthma of any classification.
* Clinically significant uncontrolled illness.
* Active infection requiring intravenous antibiotics or antifungals within 14 days prior to start of study treatment.
* Known history of immunodeficiency virus (HIV) or hepatitis B or hepatitis C infection.
* Grade \>= 3 peripheral neuropathy, or grade \>= 2 with pain on clinical examination during the screening period.
* Evidence of current uncontrolled cardiovascular conditions, including cardiac arrhythmias, congestive heart failure, angina, or myocardial infarction within the past 6 months. Note: Prior to study entry, any electrocardiogram (ECG) abnormality at screening must be documented by the investigator as not medically relevant.
* Other active malignancy. Exceptions: Non-melanoma skin cancer, ductal breast carcinoma in situ (DCIS) or carcinoma-in-situ of the cervix. Note: If there is a history or prior malignancy, they must not be receiving other specific treatment for their cancer. Prior malignancy treated with curative intent is not an exclusion.
* Females only: Pregnant or breastfeeding.
* Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures.
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics).