A Study of LN-144 or LN-145 in People With Advanced Uveal Melanoma, Undifferentiated Pleomorphic Sarcoma, Dedifferentiated Liposarcoma, or Angiosarcoma

Inclusion Criteria: * Cohort 1: Must have a confirmed diagnosis of metastatic Uveal Melanoma. o Patients will be eligible regardless of the number of prior systemic therapies received. * Cohort 2: Must have a confirmed diagnosis of unresectable or metastatic undifferentiated pleomorphic sarcoma (UPS) or dedifferentiated liposarcoma (DDLPS) that is refractory to at least 1 prior line of systemic therapy * Unresectable disease will be defined by an expert sarcoma surgical oncologist as either (a) low likelihood of obtaining an R0 resection or (b) unacceptable morbidity from a surgical procedure * Prior systemic therapy in the neoadjuvant or adjuvant setting will count has prior systemic therapy * Patients who refuse standard of care chemotherapy will be eligible * Cohort 3: Must have a confirmed diagnosis of unresectable or metastatic angiosarcoma that is refractory to at least 1 prior line of systemic therapy * Unresectable disease will be defined by an expert sarcoma surgical oncologist as either (a) low likelihood of obtaining an R0 resection or (b) unacceptable morbidity from a surgical procedure * Prior systemic therapy in the neoadjuvant or adjuvant setting will count has prior systemic therapy * Patients who refuse standard of care chemotherapy will be eligible * One (1) lesion at least 1.5cm in size (solitary or aggregate) available for TIL harvesting that has not undergone prior embolization or RT in prior 3 months unless subsequent growth is demonstrated (at least 0.5cm). * Patients must be ≥ 18 years of age at the time of consent. * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Patients must have an estimated life expectancy of ≥ 6 months in the opinion of the Investigator. * Patients must have the following hematologic parameters: * Absolute neutrophil count (ANC) ≥ 1000/mm3 * Hemoglobin (Hb) ≥ 9.0 g/dL * Platelet ≥ 100,000/mm\^3 Note: Transfusions or growth factors are not allowed 28 days prior to signing the ICF and continuing through the Screening Period * Patients must have adequate organ function: * Serum alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 times the upper limit of normal (≤ 3 × ULN); patients with liver metastasis ≤ 5 × ULN * Estimated creatinine clearance (eCrCl) ≥ 40 mL/min using the Cockcroft-Gault formula at Screening * Total bilirubin ≤ 2 mg/dL * Patients with Gilbert's syndrome must have a total bilirubin ≤ 3 mg/dL * Patients must be seronegative for the following: * Human immunodeficiency virus (HIV)-1 or HIV-2 antibodies * Hepatitis B antigen (HBsAg), hepatitis B core antibody (anti- HBc), or hepatitis C antibody (HCV Ab). Patients with acute or chronic hepatitis infections may be enrolled if the viral load by polymerase chain reaction (PCR) is undetectable with/without active treatment. * Syphilis (Rapid Plasma Reagin \[RPR\] test or venereal disease research laboratory \[VDRL\] test) * Cytomegalovirus (CMV) IgM antibody titer or PCR assay; and Epstein-Barr virus (EBV) IgM or PCR assay indicating active infection * Herpes simplex virus (HSV)-1 and HSV-2 IgM serology or PCR assay * Patients who are HSV immunoglobulin M (IgM) or PCR assay positive will need to receive appropriate treatment and become IgM or PCR assay negative prior to starting the NMA-LD pre-conditioning regimen * Anyone with prior COVID-19 infection must be asymptomatic for \>30 days prior to NMA-LD. * Patients must have a washout period from prior anticancer therapy(ies) of a minimum duration, as detailed below prior to the first study treatment (ie, start of NMA-LD): * Targeted therapy: prior targeted therapy with an EGFR, MEK, BRAF, ALK, ROS1, or other-targeted agents (eg, erlotinib, afatinib, dacomitinib, osimertinib, crizotinib, ceritinib, lorlatinib) is allowed provided the washout is a minimum of 14 days or 5 half-lives (whichever is longer) prior to the start of treatment * Chemotherapy: minimum of 21 days prior to the start of treatment * Immunotherapy: checkpoint-targeted therapy with an anti PD-1/anti PD-L1, other monoclonal antibodies, or vaccines are allowed, provided the washout is a minimum of 21 days prior to the start of study treatment * Palliative radiation therapy is permitted so long as it does not involve lesions being selected for TIL, or as target or non-target lesions. Washout is not required if all related toxicities have resolved to ≤ Grade 1 as per CTCAE v 5.0. * Patients must have recovered from all prior anti-cancer therapy-related adverse events (AEs) to ≤ Grade 1 (per Common Terminology Criteria for Adverse Events \[CTCAE\] v 5.0), except for alopecia or vitiligo, prior to enrollment. * Patients with documented ≥ Grade 2 diarrhea or colitis as a result of previous treatment with immune checkpoint inhibitor(s) must have been asymptomatic for at least 6 months and/or had a normal colonoscopy post-immune checkpoint inhibitortreatment, by visual assessment, prior to tumor resection. * Patients with immunotherapy-related endocrinopathies (e.g. hypothyroidism) stable for at least 6 weeks and controlled with hormonal replacement are allowed. * Previous surgical procedure(s) is/are permitted provided that wound healing has occurred, all complications have resolved, and at least 14 days have elapsed (for major operative procedures) prior to the tumor resection. * Patients of childbearing potential (or female partners of male participants) must be willing to take the appropriate precaution to avoid pregnancy or fathering a child for the duration of the study and practice an approved, highly effective method of birth control during treatment and for 12 months after their last dose of IL-2. Approved methods of birth control are as follows: * Combined (estrogen and progesterone containing) hormonal birth control associated with inhibition of ovulation: oral, intravaginal, transdermal * Progesterone-only hormonal birth control associat