Inclusion Criteria:  Age >= 18 years Phase I: Relapsed or refractory multiple myeloma with at least one prior line of therapy that includes a proteasome inhibitor and an immunomodulatory drug. Patient should be refractory to lenalidomide Phase II: Previously untreated multiple myeloma (diagnosed by International Myeloma Working Group [IMWG] criteria) or have received no more than one cycle of Standard of Care treatment regimen Note: Prior radiation therapy for the treatment of solitary plasmacytoma is permitted. Prior therapy with clarithromycin, dehydroepiandrosterone (DHEA), anakinra, pamidronate or zoledronic acid is permitted. Any additional agents not listed must be approved by the principal investigator  Measurable disease  Note: Phase I patients can enter trial with M spike >= 0.5 g/dl Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 Hemoglobin >= 9.0 g/dL (obtained =< 14 days prior to registration) Absolute neutrophil count (ANC) >= 1200/mm^3 (obtained =< 14 days prior to registration) Platelet count >= 100,000/mm^3 (obtained =< 14 days prior to registration) Total bilirubin =< 1.5 x upper limit of normal (ULN) (obtained =< 14 days prior to registration) Alanine aminotransferase (ALT) and aspartate transaminase (AST) =< 2.5 x ULN (=< 5 x ULN for patients with liver involvement) (obtained =< 14 days prior to registration) Prothrombin time (PT)/International Normalized Ratio (INR)/activated partial thromboplastin time (aPTT) =< 1.5 x ULN OR if patient is receiving anticoagulant therapy and INR or aPTT is within target range of therapy (obtained =< 14 days prior to registration) Calculated creatinine clearance >= 30 ml/min using the Cockcroft-Gault formula (obtained =< 14 days prior to registration)  Female participants: Female participant is eligible to participate if she is not pregnant or breast feeding, and at least one of the following conditions applies:  Is not a woman of childbearing potential (WOCBP) OR  Due to lenalidomide being a thalidomide analogue with risk for embryofetal toxicity and prescribed under a pregnancy prevention/controlled distribution program, and bortezomib having the potential to cause fetal harm, WOCBP participants will be eligible if they commit to either:  Abstain continuously from heterosexual sexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent OR  To use birth control as follows:  Two methods of reliable birth control (one method that is highly effective and one additional effective (barrier) method), beginning 4 weeks prior to initiating treatment with lenalidomide, during therapy, during dose interruptions and continuing for 4 weeks following discontinuation of lenalidomide treatment. Thereafter, WOCBP participants must use one method of reliable birth control that is highly effective for a further 4 months following discontinuation of belantamab mafodotin or a further 2 months after discontinuation of daratumumab. WOCBP must also agree not to donate eggs (ova, oocytes) for the purpose of reproduction during treatment, during dose interruptions and for 28-days following the last dose of lenalidomide, or 4 months following discontinuation of belantamab mafodotin treatment, whichever is longer.  Note: The Investigator is responsible for review of medical history, menstrual history, and recent sexual activity to decrease the risk for inclusion of a woman with an early undetected pregnancy  Male participants: Male participants are eligible to participate if they agree to the following from the time of first dose of study treatment until 28-days after the last dose of lenalidomide, or 6 months after the last dose of belantamab mafodotin, whichever is longer, to allow for clearance of any altered sperm:  Refrain from donating sperm PLUS either Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent OR  Must agree to use contraception/barrier as detailed below:  Agree to use a male condom, even if they have undergone a successful vasectomy, and female partner to use an additional highly effective contraceptive method with a failure rate of < 1% per year as when having sexual intercourse with a woman of childbearing potential (including pregnant females) Ability to understand the study procedures and provide written informed consent  Negative hepatitis B test (defined by a negative test for hepatitis B surface antigen [HBsAg], or antibodies to hepatitis B surface and/or core antigens [antiHBs or antiHBc])  Note: Participants with serologic findings suggestive of HBV vaccination (antiHBs positivity as the only serologic marker) AND a known history of prior hepatitis B virus (HBV) vaccination do not need to be tested for HBV deoxyribonucleic acid (DNA) by polymerase chain reaction (PCR). Those who are PCR positive will be excluded from the study Participant agrees not to use contact lenses while participating in the study Willingness to provide mandatory bone marrow and blood specimens for research Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) All prior treatment-related toxicities (defined by National Cancer Institute Common Toxicity Criteria for Adverse Events (NCI-CTCAE), version 5.0) must be =< grade 1 at the time of enrolment except for alopecia  Exclusion Criteria:  Monoclonal gammopathy of undetermined significance or smoldering multiple myeloma Major surgery =< 28 days prior to registration Plasmapheresis =< 14 days prior to registration  Diagnosed or treated for another malignancy =< 2 years prior to registration or previously diagnosed with another malignancy and have any evidence of residual disease  Note: Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection Note: If there is a history of prior malignancy, they must not be receiving other specific treatment (hormone therapy, chemotherapy, or immunotherapy) for their cancer Receiving any other concurrent chemotherapy, systemic steroids, any ancillary therapy considered investigational for treatment of multiple myeloma, or receiving radiotherapy =< 14 days or five half-lives, whichever is shorter, prior to first dose of study treatment. Note: Bisphosphonates are considered to be supportive care rather than therapy and are thus allowed while on protocol treatment Known to be human immunodeficiency virus (HIV) positive  Presence of positive hepatitis C antibody test result or positive hepatitis C ribonucleic acid (RNA) test result at screening or within 3 months prior to first dose of study treatment  Note: Participants with positive hepatitis C antibody due to prior resolved disease can be enrolled, only if a confirmatory negative Hepatitis C RNA test is obtained Note: Hepatitis RNA testing is optional and participants with negative hepatitis C antibody test are not required to also undergo hepatitis C RNA testing  Uncontrolled intercurrent illness including, but not limited to:  Ongoing or active infection (defined as infection undergoing treatment) Active mucosal or internal bleeding Social situations that would limit compliance with study requirements. Corneal epithelial disease (except for mild changes in the corneal epithelium) Known gastrointestinal disease (including difficulty swallowing) or gastrointestinal procedure that could interfere with the oral absorption or tolerance of lenalidomide or dexamethasone Unstable liver or biliary disease defined by the presence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, esophageal or gastric varices, persistent jaundice, or cirrhosis. Note: Stable non-cirrhotic chronic liver disease (including Gilbert's syndrome or asymptomatic gallstones) or hepatobiliary involvement of malignancy is acceptable if otherwise meets entry criteria Active renal condition (infection, requirement for dialysis or any other condition that could affect participant's safety). Note: Participants with isolated proteinuria resulting from MM are eligible, provided they fulfill inclusion criteria  Evidence of cardiovascular disease risk, as defined by any of the following:  Evidence of current clinically significant uncontrolled arrhythmias, including clinically significant electrocardiogram (ECG) abnormalities such as 2nd degree (Mobitz Type II) or 3rd degree atrioventricular (AV) block History of myocardial infarction, acute coronary syndromes (including unstable angina), coronary angioplasty, or stenting or bypass grafting =< 90 days prior to registration Class III or IV heart failure as defined by the New York Heart Association functional classification system Uncontrolled hypertension History of myocardial infarction, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias Known allergies, hypersensitivity, or intolerance to corticosteroids, monoclonal antibodies or human proteins, or their excipients (refer to respective package inserts or Investigator's Brochure) or known sensitivity to belantamab mafodotin or drugs chemically related to belantamab mafodotin, or any of the components of the study treatment