The primary objective of this phase III trial is to evaluate whether the combination of lurbinectedin plus doxorubicin given as first line treatment for metastatic leiomyosarcoma (LMS) prolongs the progression-free survival (PFS) by Independent Review Committee (IRC) when compared to doxorubicin administered as a single agent.

Inclusion Criteria:

1. Voluntary signed and dated written informed consent of the participants obtained before any trial-specific procedure.

2. Age ≥ 18 years.

3. Histologically confirmed diagnosis of metastatic LMS, in participants not candidates for curative resection.

4. Radiologically measurable disease according to the Response Evaluation Criteria in Solid Tumors (RECIST) v.1.1.

5. No previous systemic therapy for metastatic disease (i.e., first-line setting) and no previous anthracyclines. Note: prior chemotherapy (without anthracycline) in the context of adjuvant or neoadjuvant therapy is allowed. Prior line/s of hormone therapy in the adjuvant/metastatic setting are also allowed.

6. Eastern Cooperative Oncology Group (ECOG) performance status (PS) ≤ 1.

7. Adequate hematological, renal, metabolic and hepatic function:

   1. Hemoglobin ≥ 9.0 g/dL (participants may have received prior red blood cell [Red Blood Cell] transfusion); absolute neutrophil count (ANC) ≥ 2.0 x 10^9/L, and platelet count

      ≥ 100 x 10^9/L.

   2. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3.0 x upper limit of normal (ULN).

   3. Total bilirubin ≤ 1.5 x ULN or direct bilirubin ≤ ULN if total bilirubin is > ULN.

   4. Albumin ≥ 3.0 g/dL.

   5. Calculated creatinine clearance (CrCL) ≥ 30 mL/min (using Cockcroft and Gault's formula).

   6. Left ventricular ejection fraction (LVEF) > 50% assessed by multiple-gated acquisition scan (MUGA) or echocardiography (ECHO) or cardiac magnetic resonance imaging (MRI).

8. Wash-out periods:

   1. At least three weeks since last prior systemic treatment.
   2. At least three weeks since last prior major surgery and one week since last prior minor surgery (port placement is excluded from this wash-out period).
   3. At least two weeks since last prior radiotherapy.

9. Evidence of non-childbearing status for women of childbearing potential (WOCBP). WOCBP must agree to use a highly effective contraceptive measure up to seven months after treatment discontinuation. Fertile male participants with WOCBP partners should use condoms during treatment and for four months following the last investigational medicinal product (IMP) dose.

Exclusion Criteria:

1. Prior treatment with anthracyclines, lurbinectedin or trabectedin.

2. Known low grade leiomyosarcoma (i.e., grade I).

3. Known hypersensitivity to any of the components of the IV formulation of lurbinectedin or doxorubicin.

4. Concomitant diseases/conditions:

   1. History of cardiac disease: myocardial infarction or angina within the year prior to enrollment; severe vascular disease; or symptomatic arrhythmia despite ongoing treatment.
   2. Participants with any immunodeficiency, including those known to be infected by human immunodeficiency virus (HIV).
   3. Known chronic active hepatitis or cirrhosis. For Hepatitis B, this includes positive tests for both Hepatitis B surface antigen and quantitative Hepatitis B polymerase chain reaction (PCR). For Hepatitis C, this includes positive tests for both Hepatitis C antibody and quantitative Hepatitis C PCR.
   4. Active uncontrolled infection.
   5. Any other major illness that (including severe cardiovascular disease) or risk factors that, in the Investigator's judgment, will substantially increase the risk associated with the patient's participation in this trial.

5. Use of strong inducers of CYP3A4 activity within two weeks prior to the first infusion of lurbinectedin.

6. Prior irradiation of a RECIST v.1.1 target lesion if only one target lesion is available, unless progression of the lesion has been confirmed.

7. Known myopathy (history of resolved steroid-induced myopathy is allowed).

8. History of malignancies other than LMS within three years prior to enrollment, except for malignancies with a negligible risk of metastasis or death (e.g., 5-year OS rate >90%), such as adequately treated carcinoma in situ of the cervix, non-melanoma skin carcinoma, localized prostate cancer, non-muscle-invasive urothelial carcinomas, ductal carcinoma in situ, or stage I uterine cancer. Prior malignancies should have received curative treatment and should remain in remission. The Investigator should ensure, based on histology or clinical information, that the current metastatic sites are leiomyosarcoma and not recurrence of the original malignancy.

9. Limitation of the participant's ability to comply with the treatment or to follow-up the protocol.

10. Women who are pregnant or breast feeding and fertile participants (men and women) who are not using a highly effective method of contraception.

11. Participants in whom rapid tumor shrinkage is needed (e.g., when a tumor is close to a critical structure).