The purpose of this study is to determine a dose for future development and to evaluate the safety, pharmacokinetics, pharmacodynamics, and efficacy profiles of JNJ-42756493 in Japanese and other Asian patients with advanced or refractory solid tumors or lymphoma.

This is an open-label (identity of assigned study drug will be known), multicenter, 2-part, Phase 1 dose escalation/expansion to evaluate the safety, pharmacokinetics (study of what the body does to a drug), pharmacodynamics (study of what a drug does to the body) and clinical activity of JNJ-42756493 administered orally once daily in 21-day cycles or 28 days cycles of intermittent dosing regimen (7 days on/7 days off) to Japanese and Asian participants >=20 years of age with advanced or refractory solid tumors or lymphoma who are not candidates for approved or available therapies. Approximately 40 participants will be enrolled. In Part 1 Participants will be required to be hospitalized after the first dose on Day 1 of Cycle 1 until Day 2 of Cycle 2 (for daily continuous dosing) or until Day 14 of Cycle 1 (for intermittent dosing), however extension of hospitalization will be allowed until Day 2 of Cycle 2 according to investigators clinical judgment. The Part 1 dose-escalation phase is designed to determine the recommended Phase 2 dose (RP2D) based on safety, pharmacokinetic, and pharmacodynamic data of JNJ-42756493. Participants will be enrolled in sequential cohorts based on the 3+3 dose-escalation scheme; the first cohort will receive the starting dose and subsequent cohorts will receive increased doses of JNJ-42756493. After the last participants in each cohort completes Cycle 1, the Safety Evaluation Team (SET) will evaluate the safety and pharmacokinetic data according to protocol-defined criteria and make the decision whether to escalate the dose in a new cohort. To determine the recommended Phase 2 dose, the SET will review all safety, pharmacokinetic, and pharmacodynamic data from Part 1 before initiation of Part 2. The total number of participants enrolled in Part 1 will depend on the dose level at which the recommended Phase 2 dose is established. After the recommended Phase 2 dose is established, the Part 2 dose-expansion phase will be opened. Part 2 study will be done in a molecularly-defined subset of Participants with gastric adenocarcinoma including gastroesophageal junctions at the RP2D. In Part2, Participants can be hospitalized until Day 8 of Cycle 1 as needed. In addition, extension of hospitalization will be allowed until Day 15 of Cycle 1 according to investigator's clinical judgment. In Part 2, approximately 25 participants will be treated at the recommended Phase 2 dose as 28 days cycles of intermittent dosing regimen in order to evaluate fibroblast growth factor receptor target modulation in tumor, to further elaborate safety, pharmacokinetics, and pharmacodynamics of JNJ-42756493, as well as to evaluate preliminary clinical responses. Participants who are tolerating study drug treatment and achieve clinical responses or stable disease will continue to receive study drug at the same dose until disease progression, unacceptable toxicity, or withdrawal of consent. Serial pharmacokinetic and pharmacodynamic samples will be collected, and safety and efficacy will be monitored throughout the study.

Inclusion Criteria:

• Part 1: Histologically or cytologically confirmed solid malignancy or lymphoma that is metastatic or unresectable, and for which standard curative treatment is no longer effective
• Part 2: Histologically or cytologically confirmed gastric adenocarcinoma including gastroesophageal junctions that is metastatic, locally advanced or unresectable, and for which standard treatment is no longer effective or tolerable
• Eastern Cooperative Oncology Group performance status score 0 or 1
• Adequate bone marrow, liver, and renal function according to protocol-defined criteria within the 7 days prior to Day 1 of Cycle 1
• Laboratory values within protocol -defined parameters
• Agrees to protocol-defined use of effective contraception
• Negative urine pregnancy test (urine or serum beta human chorionic gonadotropin [beta-HCG]) at screening for women of child bearing potential

Exclusion Criteria:

• Has had chemotherapy, radiotherapy, immunotherapy, or treatment with an investigational anticancer agent within 3 weeks (nitrosoureas and mitomycin C within 6 weeks) before the first administration of study drug (localized radiation therapy for palliative purposes and ongoing luteinizing hormone-releasing hormone agonists and antagonists for patients with prostate cancer, bisphosphonates and denosumab are permitted
• History or current condition of uncontrolled cardiovascular disease as defined in the protocol
• Taking medications known to have a risk of causing QTc prolongation and Torsades de Pointes or known as strong CYP3A inhibitors or inducers
• Left ventricular ejection fraction less than (<) 50 percent (%) as assessed by echocardiography (or multi-gated acquisition [MUGA]) performed at screening
• Uncontrolled intercurrent illness including, but not limited to, poorly controlled hypertension or diabetes, ongoing active infection, psychiatric illness, or a risk of gastrointestinal perforation

Woman who is pregnant, breast-feeding, or planning to become pregnant or is a man who plans to father a child, while the participant is enrolled in this study and is within 3 or 5 months, respectively, after the last dose of the study drug

• Not recovered from reversible, clinically significant toxicity of prior anticancer therapy
• Presence of any medical condition that requires intact wound healing capacity and is expected to endanger participant safety if wound healing capacity would be severely reduced during administration of the investigational agent
• Major surgery within 4 weeks before enrollment
• Known human immunodeficiency virus infection
• Known hepatitis B or C (except hepatocellular carcinoma)
• Active, symptomatic, or untreated brain metastasis