This phase I/Ib study is designed to establish the safety and maximum tolerated dose (MTD, which will also be the recommended phase II dose (RP2D)) of the aurora kinase A inhibitor alisertib when combined with dose-adjusted (DA)-R-EPOCH (rituximab, etoposide, doxorubicin, vincristine, cyclophosphamide and prednisone) in patients with CD20-positive diffuse large B-cell lymphoma (DLBCL), transformed follicular lymphoma or Burkitt lymphoma positive for Myc gene rearrangement (Myc+). Filgrastim or peg-filgrastim is also included with each cycle of R-EPOCH. Once we identify the MTD, an expansion cohort limited to the Myc+ DLBCL population will be opened to further characterize clinical activity and safety.