Inclusion Criteria:  Phase I: Patients of any age >= 16 with documented Ewing sarcoma with disease accessible for repeated fine-needle aspiration biopsies who have relapsed after or are considered high-risk (unlikely to be cured by standard therapy) are eligible for the initial pharmacologic investigations. The previously untreated patients will be treated only with a single dose of lurbinectedin as if in a "window" protocol Patients must have a confirmed diagnosis of Ewing sarcoma, measurable evaluable disease, and have relapsed after standard chemotherapy or have high-risk metastatic disease unlikely to be cured with standard therapy (such as multiple bone metastases). a. Phase I: Patients must have documented Ewing sarcoma with disease accessible for repeated fine-needle aspiration biopsies. b. Phase II: Patients must have relapsed after initial curative or palliative therapy. Disease accessible for repeated biopsies is not required Phase II: Patients of any age >= 16 with documented Ewing sarcoma who have relapsed after initial curative or palliative therapy are eligible. Disease accessible for repeated biopsies is not required Patients may have any translocation type, but a sufficient number of EWS-FLI1 patients to meet objectives 1, 3, and 4 is required for study completion Prior treatment with irinotecan is permitted Estimated life expectancy of greater than 3 months Eastern Cooperative Oncology Group (ECOG) performance status =< 2 Patients must be >= 2 weeks beyond treatment of any chemotherapy, other investigational therapy, biological, targeted agents or radiotherapy, and must have recovered to =< grade 1 toxicity or previous baseline for each toxicity Abnormal organ function is permitted Absolute neutrophil count >= 1500/mL Platelets >= 100,000/mL unless due to bone-marrow infiltration by tumor Creatinine =< 1.5 x upper limit of normal (ULN) (or calculated glomerular filtration rate [GFR] > 30 ml/min) Bilirubin =< 1.6 mg/dL (1.5 x ULN) or direct bilirubin =< 0.3 mg/dL Aspartate transaminase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and/or alanine transaminase (ALT)/serum glutamic-pyruvic transaminase (SGPT) =< 2.5 x upper limit of normal (ULN) International normalized ratio (INR) =< 2 Albumin >= 3.0 g/dL  Women of childbearing potential (WOCBP) MUST have a negative serum or urine human chorionic gonadotropin (hCG) test unless prior hysterectomy or menopause (defined as 12 consecutive months without menstrual activity). Patients should not become pregnant or breastfeed while on this study. Sexually active patients must agree to use contraception prior to study entry, for the duration of study participation, and for 3 months after the last dose. Highly effective contraception methods include combination of any two of the following:  Use of oral, injected or implanted hormonal methods of contraception or Placement of an intrauterine device (IUD) or intrauterine system (IUS); Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/ vaginal suppository; Total abstinence or male/female sterilization During Phase 1, the multiple fine needle aspirations must be safe and feasible, and patients must consent to the performance of those multiple fine needle aspirations Signed informed consent obtained prior to any screening procedures  Exclusion Criteria:  Patients may not be receiving any other investigational agents Patients who are pregnant or breastfeeding Male patients whose sexual partner(s) are WOCBP who are not willing to use adequate contraception, during the study and for 6 months after the end of treatment Patients with uncontrolled intercurrent illness including, but not limited to active infection requiring hospitalization Active (acute or chronic) or uncontrolled severe infection, liver disease such as cirrhosis, decompensated liver disease, and chronic hepatitis (i.e. quantifiable hepatitis B virus [HBV]-deoxyribonucleic acid [DNA] and/or positive hepatitis B virus surface antigen [Hbs/Ag], quantifiable hepatitis C virus [HCV]-ribonucleic acid [RNA]) Active, bleeding diathesis Known history of human immunodeficiency virus (HIV) seropositivity Patients with a history of non-compliance to medical regimens or who are considered potentially unreliable or will not be able to complete the entire study Patients who are currently part of or have participated in any clinical investigation with an investigational drug within 1 month prior to dosing Prior treatment with PM01183, or trabectedin Evident symptomatic pulmonary fibrosis or interstitial pneumonitis, pleural or cardiac effusion rapidly increasing and/or necessitating prompt local treatment within seven days Known hypersensitivity to irinotecan