Ipilimumab and Nivolumab for the Treatment of Stage III-IV Unresectable Metastatic Melanoma

Inclusion Criteria: * Age \>=18 years * Measurable disease as defined below: * A non-nodal lesion is considered measurable if its longest diameter can be accurately measured as \>= 2.0 cm with chest x-ray, or as \>= 1.0 cm with computed tomography (CT) scan, CT component of a positron emission tomography (PET)/CT, or magnetic resonance imaging (MRI) * A superficial non-nodal lesion is measurable if its longest diameter is \>= 1.0 cm in diameter as assessed using calipers (e.g., skin nodules) or imaging. In the case of skin lesions, documentation by color photography, including a ruler to estimate the size of the lesion, is recommended. * A malignant lymph node is considered measurable if its short axis is \> 1.5 cm when assessed by CT scan (CT scan slice thickness recommended to be no greater than 5 mm). * NOTE: Tumor lesions in a previously irradiated area are not considered measurable disease. * Histologically or cytologically confirmed diagnosis of unresectable stage III or IV metastatic melanoma, meeting one of the following criteria: * Progressed after at least one line of FDA approved therapy \[either immune checkpoint inhibitor (ICI) or targeted therapy\] * Recurrent disease following initial surgical resection (may or may not have received adjuvant therapy) * Newly diagnosed or recurrent in-transit metastatic melanoma (may or may not be treatment naïve) * Progressed on at least one line of therapy containing anti-PD-1, antiPD-L1, or a BRAF inhibitor * Hemoglobin \>= 8.0 g/dL (obtained =\< 15 days prior to registration) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 15 days prior to registration) * Platelet count \>= 75,000/mm\^3 (obtained =\< 15 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 15 days prior to registration) * Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3.0 x ULN (obtained =\< 15 days prior to registration) * Serum creatinine =\< 2.0 x ULN (obtained =\< 15 days prior to registration) * Calculated creatinine clearance \>= 40 ml/min using the Cockcroft-Gault formula (obtained =\< 15 days prior to registration) * Prothrombin time (PT)/institutional normalized ratio (INR)/activated partial thromboplastin time (aPTT) =\< 1.5 x ULN OR if patient is receiving anticoagulant therapy INR or aPTT is within target range of therapy (obtained =\< 15 days prior to registration) * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1 * Negative pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only * Persons able to become pregnant OR able to father a child must be willing to use an adequate method of contraception while on treatment and for 180 days (6 months) after last treatment dose on this study * Provide written informed consent * Patients enrolling in Rochester, Minnesota (MN), ONLY: Willingness to provide mandatory blood specimens for correlative research * Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) Exclusion Criteria: * Metastatic sites that drain lymphatic fluid into nodal beds which are not amenable to lymphatic infusion * Sites of metastases limited only to the head and neck * Sites of metastatic disease limited to the lungs and/or hilar lymph nodes * Metastatic uveal melanoma * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant persons * Nursing persons * Persons of childbearing potential who are unwilling to employ adequate contraception * Persons expecting to conceive or father children during the study or within 180 days (6 months) after the last treatment on this study * Active central nervous system (CNS) metastases not previously treated * NOTE: patients with history of previously treated CNS metastases, not demonstrating evidence of progression for at least 12 weeks will be allowed * NOTE: patients with leptomeningeal metastases are not eligible * Any of the following prior therapies: * Allogeneic hematopoietic stem cell transplantation (HSCT) * Solid organ transplantation * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy. * NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial * Active autoimmune disease requiring systemic treatment \< 2 years prior to registration, documented history of severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents with use of disease modifying agents, corticosteroids or immunosuppressive drugs. NOTE: Exceptions are allowed for the following conditions: * Vitiligo * Resolved childhood asthma/atopy * Intermittent use of bronchodilators or inhaled steroids * Daily steroids at dose of =\< 10 mg of prednisone (or equivalent) * Local steroid injections * Stable hypothyroidism on replacement therapy * Stable diabetes mellitus on therapy (with or without insulin) * Sjogren's syndrome * Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) which is not considered a form of systemic treatment and is allowed * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection requiring systemic therapy * Interstitial lung disease * Serious, chronic gastrointestinal conditions associated with diarrhea (e.g., Crohn's disease or others) * Known history of hepatitis B (i.e., known positive hepatitis B virus (HBV) surface antigen (HBsAg) reactive) * Known active hepatitis C (i.e., positive for hepatitis C virus (HCV) ribonucleic acid (RNA) detected by polymerase chain reaction (PCR)) * Known active tuberculosis (TB) * Symptomatic congestive heart failure * Unstable angina pectoris * Unstable cardiac arrhythmia or * Psychiatric illness/social situations that would limit compliance with study requirements (e.g., known substance abuse) * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * History of severe hypersensitivity reactions to other monoclonal antibodies or known hypersensitivity to the study intervention or its excipients, indocyanine green (ICG) dye or iodine * Prior history of grade 4 immune related adverse event (irAE) with prior intracavernosal injection (ICI) therapy or failure to recover (\< grade 1) from immune-related adverse event(s) from prior ICI therapy * Any of the following therapies prior to registration: * Chemotherapy =\< 28 days * Immunotherapy =\< 28 days * Targeted therapies (e.g., dabrafenib) =\< 21 days * Other investigational agents =\< 28 days * Radiation therapy =\< 14 days * Minor surgical or interventional procedure =\< 7 days * Major surgical procedure =\< 21 days