A Study of LY2880070 and Gemcitabine in People With Ewing Sarcoma,Ewing-Like Sarcoma, and Desmoplastic Small Round Cell Tumor

Inclusion Criteria: * Consent/Assent: all patients and/or their parents or legally authorized representatives must sign written informed consent; assent, when appropriate, will be obtained according to institutional guidelines * Weight/Age: patients must be ≥40 kg at the time of study enrollment, but may be of any age * Diagnosis: Patients must have histologically documented locally advanced or metastatic disease confirmed at MSK as follows: * Main cohort: Ewing sarcoma as molecularly defined by an EWSR1 fusion with an ETS-transcription factor family member including FLI1, ERG, ETV1, ETV4, and FEV * Pilot cohort: Ewing-like sarcomas including CIC-rearranged sarcoma, BCOR-rearranged sarcoma, and sarcomas with a rearrangement between EWSR1 and a non-ETS family gene or desmoplastic small round cell tumor as molecularly defined by an EWSR1-WT1 fusion Note: Any patient being enrolled into the pilot cohort that does not have a CIC, BCOR- rearranged sarcoma, or desmoplastic small round cell tumor will be reviewed with study pathologist, Dr. Cristina Antonescu, to ensure the categorization as Ewing-like sarcoma is appropriate * Patients must be able to swallow capsules * Therapeutic options: patient's current disease state must be one which has failed standard cytotoxic chemotherapy including cyclophosphamide/doxorubicin/vincristine and ifosfamide/etoposide * Disease Status: patients must have measurable disease based on RECIST 1.1 * Performance level: Karnofsky ≥70% for patients \>16 years of age and Lansky ≥70 for patients ≤16 years of age * Prior Therapy: patients may have had any number of regimens and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment Note: Patients who have previously received gemcitabine will be allowed unless they had hypersensitivity or unacceptable toxicity attributed to gemcitabine * ≥ 21 days must have elapsed after the last dose of cytotoxic or myelosuppressive chemotherapy and patients must have recovered from the acute toxic effects of these agents (other than alopecia) * ≥ 14 days must have elapsed after radiation therapy, and toxicity related to prior radiation therapy must be recovered to grade ≤ 1 * ≥ 21 days must have elapsed after the last dose of antibody therapy, and toxicity related to prior antibody therapy must be recovered to grade ≤ 1 Organ Function Requirements: * Adequate bone marrow function defined as: * Absolute neutrophil count (ANC) ≥ 1500/mm3 * Platelet count ≥ 100,000/mm3 * Hemoglobin ≥ 8 g/dl * Adequate renal function defined as estimated glomerular filtration (eGFR) rate ≥ 60 mL/min/1.73m2: * as estimated by CKD-EPI equation for patients ≥ 18 years of age OR * As estimated by cystatin C for patients \< 18 years of age * Adequate liver function defined as: * Bilirubin (sum of conjugated + unconjugated) ≤ 1.5 x upper limit of normal for age * AST or ALT ≤ 2.5 x upper limit of normal for patients without liver metastases * AST or ALT ≤ 5 x upper limit of normal for patients with liver metastases * Serum albumin ≥ 2.5 g/dl * Adequate cardiac function defined as: * Left ventricular ejection fraction (LVEF) \>45% as measured on echocardiogram, cardiac MRI, or MUGA * QTc \< 470 ms on screening 12 lead electrocardiogram * Pregnancy/Contraception * Post-menarchal females must have a negative urine or serum pregnancy test at screening and ≤ 24 hours prior to study treatment * Males or females of reproductive potential must be willing to use a barrier method of contraception throughout the course of the study and for 6 months after completing study treatment Exclusion Criteria: * Patients for whom the investigator deems that gemcitabine is not appropriate * Patients who have an uncontrolled infection * Central Nervous System (CNS) Metastases * Patients who have symptomatic central nervous system (CNS) metastases. Note: patients with treated and asymptomatic CNS metastases are eligible. * Patients with CNS metastases requiring corticosteroids for management * If the treatment of CNS disease requires anticonvulsants, the dose must have been stable for ≥ 4 weeks. * Patients who are pregnant or breast feeding * Patients who have a history of Torsades de Pointes, carry a diagnosis of congestive heart failure, or have a family history of prolonged QT syndrome * Patients who, in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study * Patients with known hypersensitivity to gemcitabine