• To determine the maximum tolerated dose (MTD) and recommended Phase 2 dose (RP2D) of a 3-hour intravenous (IV) infusion of RH-1 administered once every 21 days. [ Time Frame: Study duration ] [ Designated as safety issue: Yes ]
  

• To evaluate the safety and tolerability of 3-hour IV infusions of RH-1. [ Time Frame: Study duration ] [ Designated as safety issue: Yes ]
  
• To determine the pharmacokinetic (PK) profile of 3-hour IV infusions of RH-1 administered at escalating doses. [ Time Frame: Study duration ] [ Designated as safety issue: No ]
  
• To assess preliminary evidence of anti-cancer activity of RH-1. [ Time Frame: Study duration ] [ Designated as safety issue: No ]
  
• To explore evidence of differential deoxyribonucleic acid (DNA) cross-linking and downstream phenotypic consequences of RH-1 exposure in peripheral blood mononuclear cells (PBMCs), circulating tumor cells (CTCs), and tumor biopsies. [ Time Frame: Study duration ] [ Designated as safety issue: No ]
  
• To explore the correlation and possible significance of germline polymorphisms in NAD(P)H:quinone oxidoreductase (NQO1) and DNA cross-linking as consequences of RH-1 exposure in PBMCs, CTCs, and tumor biopsies, as markers of anticancer activity. [ Time Frame: Study duration ] [ Designated as safety issue: No ]
  

Inclusion Criteria:

1. Histologically proven advanced solid tumors or NHL, relapsed or refractory to conventional treatment, or for which no conventional therapy exists or is considered acceptable for the patient.
2. Tumor accessible for biopsy (required in expanded cohort of 24 patients only; optional in all other patients).
3. At least 18 years of age.
4. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1.
5. Life expectancy ≥ 3 months.
6. Adequate hematological, hepatic, and renal function as defined by the following: absolute neutrophil count (ANC) ≥ 1.5 x 109/L, platelet count ≥ 100 x 109/L, total bilirubin ≤ 1.5 × the upper limit of normal (ULN), aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 × ULN (AST/ALT ≤ 5 × ULN if documented hepatic involvement), creatinine ≤ 1.5 mg/dL or if serum creatinine is elevated then patient has a calculated creatinine clearance ≥ 50 mL/min.
7. Toxic manifestations of previous treatment(s) have resolved, with the exceptions of ≤ Grade 2 fatigue if stable for > 2 months, ≤ Grade 2 alopecia and/or other Grade 1 toxicities, which in the opinion of the investigator should not exclude the patient (eg, palmar erythema; stable Grade 1 peripheral neuropathy).
8. Women of child-bearing potential must have a negative serum pregnancy test within 14 days prior to the first day of study treatment. Women who are postmenopausal for at least 1 year (defined as > 12 months since last menses) or are surgically sterilized do not require this test. Women of child-bearing potential and their male partners must agree to practice a medically acceptable contraceptive regimen from study treatment initiation until at least 30 days after the last administration of RH-1. Adequate methods of contraception are double barrier methods (condoms with spermicidal jelly or foam, and diaphragm with spermicidal jelly or foam), oral, depot and injectable contraceptives, and intrauterine device (IUD). RH-1 should not be administered to women who are breast feeding.
9. Men who are not surgically sterile must agree to practice a medically acceptable contraceptive regimen from study treatment initiation until at least 90 days after the last administration of RH-1.
10. Given written informed consent (IC).

Exclusion Criteria:

1. Active concurrent malignancy, with the exception of adequately treated carcinoma in situ of the cervix and/or basal or squamous cell carcinoma of the skin. If there is a history of prior malignancy, the patient must be disease-free for ≥ 5 years.
2. Receipt of any investigational or conventional chemotherapy, targeted therapy, endocrine therapy, or immunotherapy within 4 weeks prior to study treatment or planned use during the course of the study. Hormonal therapy (gonadotropin-releasing hormone analog [leuprolide] for prostate cancer, somatostatin analog [octreotide] for carcinoid tumor, and anti-estrogens for breast cancer) will be allowed if the drug administration has been stable for ≥ 4 weeks.
3. Use of any radiation therapy (RT) within 28 days prior to study treatment or planned use during the course of the study.
4. Requires therapeutic levels of anticoagulation therapy.
5. Failed treatment with a bone marrow transplant.
6. Active uncontrolled infection, underlying medical condition such as patients at poor medical risk because of non-malignant systemic disease, or other serious illness that would impair the ability of the patient to receive protocol treatment.
7. Known to be positive for Hepatitis B, Hepatitis C, or human immunodeficiency virus (HIV).
8. Symptomatic central nervous system (CNS) metastases or lesions for which treatment is required.
9. Major surgery within 4 weeks of planned start of treatment.
10. Previous exposure to RH-1.