Normal pulmonary function tests (including diffusing capacity of the lungs for carbon monoxide [DLCO]) if there is clinical indication for determination (e.g. dyspnea at rest, known requirement for supplemental oxygen); Note: for patients who do not have respiratory symptoms or requirement for supplemental oxygen, pulmonary function tests (PFTs) are NOT required Diffusion capacity of the lung for carbon monoxide (DLCO) > 40% with no symptomatic pulmonary disease Patients must have pulmonary function sufficient to receive bleomycin, with normal lung expansion, absence of crackles on auscultation, and normal carbon monoxide diffusion (DLCO), defined as greater than 80% predicted Patients must have pulmonary function tests (PFTs) including forced expiratory volume in 1 second (FEV1) within 84 days prior to registration; for FEV1, the best value obtained pre- or post-bronchodilator must be >= 1.2 liters/second and/or >= 50% predicted Known history of uncontrolled sleep apnea syndrome and other conditions that could result in excessive daytime sleepiness, such as severe chronic obstructive pulmonary disease; requirement for supplemental oxygen, or any conditions that could result in excessive toxicity associated with the benzodiazepine-like effects of MLN8237 History of pulmonary disease such as emphysema or chronic obstructive pulmonary disease (COPD), (forced expiratory volume [FEV] > 60% of predicted for height and age required in patients with prolonged smoking history or symptoms of respiratory dysfunction) Ejection fraction (EF) < 40% or myocardial infarction (MI) within the past 3 months; known history of uncontrolled sleep apnea syndrome and other conditions that could result in excessive daytime sleepiness, such as severe chronic obstructive pulmonary disease; requirement for supplemental oxygen; or any conditions that could result in excessive toxicity associated with the benzodiazepine-like effects of MLN8237 Patients must have forced expiratory volume in 1 second (FEV1)/forced vital capacity (FVC) > 60% by pulmonary function test (PFT), unless due to large mediastinal mass from HL; carbon monoxide diffusion capacity (DLCO), FEV1, and FVC all > 50% predicted value; all pulmonary function tests must be obtained within one month prior to registration RANDOMIZED PHASE II (ARMS K AND L): Patients must have FEV1/FVC > 60% by pulmonary function test (PFT), unless due to large mediastinal mass from HL; carbon monoxide diffusion capacity (DLCO), FEV1, and FVC all > 50% predicted value; all pulmonary function tests must be obtained within one month prior to registration Diffusing capacity of the lung for carbon monoxide (DLCO)/alveolar volume (VA) and forced expiratory volume in 1 second (FEV-1.0) >= 60% of predicted on pulmonary function tests No history of severe chronic obstructive pulmonary disease (COPD) or emphysema or interstitial lung disease currently on home supplemental oxygen; patients with NSCLC with stable COPD or emphysema not requiring supplemental oxygen are eligible Pulmonary embolism Pulmonary hypertension Forced expiratory volume in 1 second (FEV1)/forced vital capacity (FVC) > 60% by pulmonary function test (PFT), unless due to large mediastinal mass from Hodgkin lymphoma (HL) Diffusion capacity of the lung for carbon monoxide (DLCO) >= 40% of predicted (corrected or uncorrected for hemoglobin per institutional standards) Forced expiratory volume in 1 second (FEV1) >= 40% of predicted (corrected or uncorrected for hemoglobin per institutional standards) Forced vital capacity (FVC) >= 40% of predicted (corrected or uncorrected for hemoglobin per institutional standards) Adequate pulmonary function as assessed by oxygen saturation >= 90% when ambulating and not requiring supplemental oxygen Forced expiratory volume in 1 second (FEV-1) or diffusion capacity of the lung for carbon monoxide (DLCO) (corrected for hemoglobin) >= 50% predicted; timeline: within 4 weeks prior to enrollment Resting oxygen saturation (O2 sat) must be >= 92% Diffusing capacity divided by the alveolar volume (DDLCO/VA) and forced expiratory volume (FEV) 1.0 > 50% of predicted on pulmonary function tests Oxygen saturation >= 90% when ambulating and not requiring supplemental oxygen Excluded if known active pulmonary disease with hypoxia defined as: * Oxygen saturation < 85% on room air, or* Oxygen saturation < 88% despite supplemental oxygen