ADI-PEG 20 in Combination With Gemcitabine and Docetaxel for the Treatment of Soft Tissue Sarcoma, Osteosarcoma, Ewing's Sarcoma, and Small Cell Lung Cancer

Inclusion Criteria: * Cohort 1: Histologically or cytologically confirmed grade 2 or 3 soft tissue sarcoma that is unresectable or metastatic that would be standardly treated with gemcitabine or gemcitabine and docetaxel. For all others, please contact the principal investigator. Prior surgery for primary or metastatic disease after chemotherapy following a response is allowed. * Cohort 2: Histologically or cytologically confirmed osteosarcoma, Ewing's sarcoma, or small cell lung cancer that is unresectable or metastatic that have either failed standard of care therapy or would be standardly treated with gemcitabine or gemcitabine and docetaxel. * Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with CT scan, as ≥ 20 mm by chest x-ray, or ≥ 10 mm with calipers by clinical exam. * Treated with at least one line of systemic therapy. The allowable window between treatments is 21 days for chemotherapy or a TKI, or 5 ½ half-lives for a TKI (whichever is shorter), 21 days and progression by CT for immunotherapy, 21 days for RT, 21 days for surgery, or 28 days for an investigational agent. * Cohort 1: At least 16 years of age. * Cohort 2: Patients with osteosarcoma or Ewing's sarcoma must be at least 10 years of age. Patients with small cell lung cancer must be at least 18 years of age. * Cohort 2 (SCLC group ONLY): Must be amenable to biopsy * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 * Normal bone marrow and organ function as defined below: * Leukocytes ≥ 3,000/mcL * Absolute neutrophil count ≥ 1,500/mcl * Platelets ≥ 100,000/mcl * Total bilirubin ≤ 2 x institutional upper limit of normal (IULN) * AST(SGOT)/ALT(SGPT) ≤ 3 x IULN (or ≤ 5 x IULN if liver metastases are present) * Creatinine ≤ 1.5 x IULN OR * Creatinine clearance ≥ 60 mL/min/1.73 m2 for patients with creatinine levels above institutional normal * Serum uric acid ≤ 8 mg/dL (with or without medication control) * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Exclusion Criteria: * A history of other high grade malignancy ≤ 5 years previous. Exceptions include basal cell or squamous cell carcinoma of the skin which were treated with local resection only or carcinoma in situ of the cervix, or other tumors discussed with the study PI * Currently receiving any other investigational agents. * Prior treatment with ADI-PEG 20, gemcitabine, or docetaxel. Patients treated \> one year ago in the adjuvant/neoadjuvant setting with gemcitabine or docetaxel would be allowed to be enrolled on the trial. * Known brain metastases. Patients with known brain metastases must be excluded from this clinical trial (except for patients with SCLC, see below) because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. Patients with SCLC are allowed to enroll with brain metastases provided they are stable and they are at least 3 months post-treatment for brain metastases. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to ADI-PEG 20, gemcitabine, pegylated compounds, or other agents used in the study. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * History of seizure disorder not related to underlying cancer. * Pregnant and/or breastfeeding. Women of childbearing potential must have a negative pregnancy test within 14 days of study entry. * Known HIV-positivity on combination antiretroviral therapy because of the potential for pharmacokinetic interactions with the study treatment. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.