The purpose of this study is to evaluate the safety, pharmacokinetics (study of what the body does to a drug), and pharmacodynamics (study of what a drug does to the body) of JNJ-42756493, a pan-fibroblast growth factor receptor (FGFR) tyrosine kinase inhibitor, in adult participants with advanced or refractory solid tumors or lymphoma.

This is a first-in-human, non-randomized (individuals will not be assigned by chance to study treatments), open-label (individuals will know the identity of study treatments), multicenter (more than 1 hospital work on a study), Phase 1 study. The study consists of 4 parts. Part 1 is the dose-escalation phase, which will be guided by pharmacokinetics, pharmacodynamics and safety. In part 1, safe and biologically active Phase 2 doses (recommended Phase 2 doses [RP2D]) for JNJ-42756493 will be primarily assessed. Participants will be enrolled in sequential cohorts (first cohort will receive the starting dose and subsequent cohorts will receive increased doses of JNJ-42756493). Part 2 is the Dose Confirmation Phase, which consists of a pre and post treatment tumor biopsy cohorts to confirm the RP2D based on the pharmacodynamic effect of JNJ-42756493 on fibroblast growth factor receptor (FGFR) signaling pathway in tumor. Part 3 is the first Dose Expansion Phase, which is designed to evaluate inclusion biomarkers and preliminary clinical activity at the first RP2D. It consists of 4 expansion cohorts, 1 each for squamous cell lung cancer, small cell lung cancer, breast cancer, other solid tumors (Cohorts A, B, C, and D). Part 4 is the second Dose Expansion Phase, which is designed to evaluate inclusion biomarkers and preliminary clinical activity at the second RP2D. Biomarker eligibility has also been refined based on emerging data. It consists of 2 expansion cohorts, Cohort E for non-small cell lung cancer and Cohort F for select solid tumors including breast, urothelial, GBM, ovarian, head & neck, esophageal, gastric, and cholangiocarcinoma (Cohorts E and F). Enrollment of some cohorts may be discontinued due to lack of enrollment or for futility. The study is estimated to take approximately 48 months to complete. Participants' safety will be monitored throughout the study.

Inclusion Criteria:

• Histologically or cytologically confirmed: solid malignancy or lymphoma that is metastatic or unresectable, and for which standard curative treatment is no longer effective (Part 1); any type of advanced or refractory solid malignancy (excluding lymphoma) that is metastatic or unresectable and for which standard curative treatment is no longer effective (Part 2); advanced or refractory squamous non-small cell lung cancer (Cohort A, Part 3), advanced or refractory small cell lung cancer (Cohort B, Part 3), advanced or refractory breast cancer (Cohort C, Part 3), any type of advanced or refractory solid malignancy (excluding lymphoma) ([consisting of one of the following: gastric, head and neck, lung adenocarcinoma, urothelial, glioblastoma multiforme (GBM), ovarian or prostate]) (Cohort D, Part 3), advanced or refractory non small cell lung cancer(Cohort E, Part 4), any type of advanced or refractory solid malignancy (consisting of one of the following: Breast, Urothelial, GBM, Ovarian, Head & Neck, Esophageal, Gastric, and Cholangiocarcinoma) (Cohort F, Part 4)
• Eastern Cooperative Oncology Group performance status score 0 or 1
• Adequate bone marrow, liver, and renal function within the 14 days prior to Day 1 of Cycle 1 of study drug up until pre-dose of Cycle 1
• Magnesium within 0.85 to 1.25 * institutional normal limits, Sodium greater than or equal to 130 milli equivalent per liter, Potassium within institutional normal limits (within 14 days prior to Day 1 of Cycle 1 up until pre-dose of Cycle 1)

Exclusion Criteria:

• Chemotherapy, targeted therapies, radiotherapy, immunotherapy, or treatment with an investigational anticancer agent within 2 weeks or at least 5 half-lives of the drug, whichever is longer and up to a maximum of 4 weeks (in the case of nitrosoureas and mitomycin C within 6 weeks) before the first administration of study drug. Localized radiation therapy and ongoing luteinizing hormone-releasing hormone (LHRH) agonists, bisphosphonates and denosumab, are permitted
• Participants with GBM can be enrolled 2 weeks after last treatment
• History or current condition of uncontrolled cardiovascular disease
• Participants with persistent phosphate greater than upper limit of normal during screening (within 14 days prior to Day 1 of Cycle 1 up until pre-dose of Cycle 1) and despite medical management of phosphate levels
• Participants taking medications known to have a significant risk of causing QTc prolongation and Torsades de Pointes
• Left ventricular ejection fraction (LVEF) less than 50 percent as assessed by echocardiography (or multi-gated acquisition) performed at screening
• 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
• Participants not recovered from reversible toxicity of prior anticancer therapy (except toxicities which are not clinically significant such as alopecia, skin discoloration, or Grade 1 neuropathy)