Lurbinectedin + Doxorubicin In Leiomyosarcoma

Inclusion Criteria: * For Enrollment to Phase 1b: Participants must have histologically confirmed advanced or metastatic soft-tissue sarcoma and no curative multimodality treatment options available. * For Enrollment to Phase 2: Participants must have histologically confirmed advanced or metastatic leiomyosarcoma (LMS) and no curative multimodality treatment options available. * Participants must have measurable disease per RECIST 1.1 criteria * Age ≥ 18 years. Because no dosing or adverse event data are currently available on the use of lurbinectedin in combination with doxorubicin in participants \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials. * ECOG performance status ≤ 2 (Karnofsky ≥ 60%,). * Participants must have adequate organ and marrow function as defined below: * Absolute Neutrophil Count ≥ 1,500/mcL * Hemoglobin (Hgb) ≥ 8 g/dl (transfusion support permitted) * Platelet Count ≥ 100,000/mcL * Total Bilirubin ≤ 1.5 × institutional upper limit of normal (ULN) * AST (SGOT) / ALT(SGPT) ≤ 2.5 × institutional ULN, OR ≤ 5 × institutional ULN if elevation is a result of metastases * Creatinine ≤ 1.5 × institutional ULN, OR Creatinine Clearance ≥ 60 mL/min/1.73 m2 for participants with creatinine levels above 1.5 × institutional normal (calculated via the Cockcroft-Gault equation) * Creatine Phosphokinase (CPK)\< 2.5 × institutional ULN on two different determinations performed one week (± 1 day) apar…