Inclusion Criteria:

        Dose Escalation Cohorts (Part 1)

          -  Has a histologically or cytologically documented advanced solid tumor or lymphoma that
             has relapsed from or is refractory to standard treatment, or for which no standard
             treatment is available.

               -  Participants with melanoma who are ineligible to receive or have declined
                  ipilimumab treatment or who are refractory or intolerant to ipilimumab may
                  enroll.

               -  Participants with certain tumor types such as those with high prevalence of MDM2
                  amplification or overexpression (eg, well-differentiated [WD]/dedifferentiated
                  [DD] liposarcoma) may be preferentially enrolled in Part 1.

        Dose Expansion Cohort (Part 2)

          -  Has a histologically or cytologically documented advanced melanoma or diffuse large B
             cell lymphoma (DLBCL), with measurable disease that is refractory to standard
             treatment or for which no standard treatment is available.

               -  Participants with melanoma who are ineligible to receive or have declined
                  ipilimumab treatment or who are refractory or intolerant to ipilimumab may
                  enroll.

               -  Participants with DLBCL who have failed, been deemed ineligible for, or refused
                  autologous stem cell transplantation may enroll.

          -  Man or woman ≥ 18 years old.

          -  Has an Eastern Cooperative Oncology Group (ECOG) performance status 0-1.

          -  Has adequate bone marrow function, defined as:

               -  Platelet count ≥ 100 x 10^9/L

               -  Hemoglobin ≥ 9.0 g/dL

               -  Absolute neutrophil count ≥ 1.5 x 10^9/L.

          -  Has adequate renal function, defined as creatinine clearance ≥ 60 mL/min, as
             calculated using the modified Cockcroft Gault equation, ([{140 - age in years} ×
             {actual weight in kg}] divided by [{72 × serum creatinine in mg/dL} multiply by 0.85
             if female]), OR creatinine ≤ 1.5 x ULN.

          -  Has adequate hepatic function, defined as:

               -  AST/ALT levels ≤ 3 x ULN (if liver metastases are present, ≤ 5 x ULN)

               -  Bilirubin ≤ 1.5 x ULN.

          -  Has adequate blood clotting function, defined as International normalized ratio (INR)
             and activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN.

          -  Participant should be able to provide written informed consent, comply with protocol
             visits and procedures, be able to take oral medication, and not have any active
             infection or comorbidity that would interfere with therapy.

          -  Participant (male and female) of childbearing/reproductive potential must agree to use
             double-barrier contraceptive measures or avoid intercourse during the study and for 90
             days after the last dose of study drug.

          -  Participant must be fully informed about their illness and the investigational nature
             of the study protocol (including foreseeable risks and possible side effects) and must
             sign and date an IRB [Institutional Review Board]-approved Informed consent Form [ICF]
             (including Health Insurance Portability and Accountability Act authorization, if
             applicable) before performance of any study specific procedures or tests.

          -  Is willing to provide and there is confirmed availability of pre-existing diagnostic
             or resected tumor samples, such as paraffin-embedded sections. Providing fresh tumor
             biopsy is optional for participants in Dose Escalation cohorts.

          -  Is willing to undergo tumor genotyping for TP53 mutation, insertion, or deletion at
             screening. Confirmation of TP53 nonmutant status is encouraged, but not required prior
             to milademetan dosing.

          -  Is willing to provide additional archived samples for comprehensive genomic and/or
             proteomic analyses if the participant has a partial response/complete response to
             milademetan treatment.

          -  Is willing to undergo pre-treatment tumor biopsies (Part 2 only)

        Exclusion Criteria:

          -  Has a tumor that contains an inactivating mutation, insertion, or deletion in the TP53
             gene determined previously or at screening.

          -  Has a history of primary central nervous system malignancy.

          -  Has gastrointestinal conditions that could affect the absorption of milademetan in the
             opinion of the Investigator.

          -  Has an uncontrolled infection requiring intravenous antibiotics, antivirals, or
             antifungals, known human immunodeficiency virus infection, or active hepatitis B or C
             infection.

          -  Has received an allogeneic bone marrow or allogeneic stem cell transplant.

          -  Has a concomitant medical condition that would increase the risk of toxicity, in the
             opinion of the Investigator or Sponsor.

          -  Has clinically active brain metastases, defined as untreated and symptomatic, or
             requiring therapy with steroids or anticonvulsants to control associated symptoms.
             Participants with treated brain metastases that are no longer symptomatic and who
             require no treatment with steroids may be included in the study if they have recovered
             from the acute toxic effect of radiotherapy. A minimum of 4 weeks must have elapsed
             between the end of whole brain radiotherapy and study enrollment (2 weeks for
             stereotactic radiotherapy).

          -  Has unresolved toxicities from previous anticancer therapy, defined as toxicities
             (other than alopecia) not yet resolved to NCI-CTCAE v4, grade ≤ 1 or baseline.
             Participants with chronic grade 2 toxicities may be eligible per the discretion of the
             Investigator and Sponsor (eg, grade 2 chemotherapy-induced neuropathy).

          -  Had an autologous transplant within 3 months of starting study drug treatment.

          -  Is receiving concomitant treatment with a strong inducer of CYP3A.

          -  Had systemic treatment with anticancer therapy, antibody-based therapy, retinoid
             therapy, or hormonal therapy within 3 weeks before study drug treatment; or treatment
             with nitrosoureas or mitomycin C within 6 weeks before study drug treatment; or
             treatment with small-molecule targeted agents within 2 weeks before study drug
             treatment. Previous and concurrent use of hormone replacement therapy, the use of
             gonadotropin releasing hormone modulators for prostate cancer, and the use of
             somatostatin analogs for neuroendocrine tumors are permitted if such therapy has not
             been changed within 8 weeks before study drug treatment.

          -  Had therapeutic radiation therapy or major surgery within 4 weeks before study drug
             treatment or palliative radiation therapy within 2 weeks before study drug treatment.

          -  Participated in a therapeutic clinical study within 3 weeks before study drug
             treatment, or current participation in other therapeutic investigational procedures.

          -  Prolongation of corrected QT interval by Fridericia's method (QTcF) at rest, where the
             mean QTcF interval is > 450 milliseconds (ms) for males and > 470 ms for females based
             on triplicate ECG.

          -  Pregnant or breastfeeding.

          -  Substance abuse or medical, psychological, or social conditions that, in the opinion
             of the Investigator, may interfere with the participant's participation in the
             clinical study or evaluation of the clinical study results.

          -  Prior treatment with an MDM2 inhibitor.