This phase Ib/II trial is aimed at studying the combination of a drug named Selinexor (selective inhibitor of nuclear export) in combination with standard therapy for B cell Non-Hodgkin's lymphoma called R-CHOP. The investigators will establish maximum tolerated dose of Selinexor in combination with RCHOP and also study the efficacy of this combination for therapy of B cell Non-Hodgkin's lymphoma. Giving Selinexor plus chemotherapy may work better in treating patients with B cell non-Hodgkin lymphoma.

The study will be done in two phases namely phase 1B and phase 2.

In the phase 1B component the investigators intend to enroll patients in a 3+3 dose escalation design. Newly diagnosed indolent and diffuse large cell lymphomas as well as relapsed/refractory indolent B cell lymphomas are eligible for enrollment in the phase 1 component. The primary end-point for this component would be to establish the recommended phase 2 dose (RP2D) for Selinexor in combination with standard dose RCHOP chemotherapy.

In the phase 2 part of the study the investigators will use recommended phase 2 dose of Selinexor plus standard dose RCHOP combination to treat newly diagnosed DLBCL patients with the primary end-point being 2 year Progression free survival.

Maintenance Phase: Patients with Follicular Lymphoma and Diffuse Large B cell lymphoma able to achieve PR or better at the end of therapy scan will be put on maintenance Selinexor for a total of one year. The dose of Selinexor in the maintenance phase would be similar to the last dose used for that particular patient in the treatment phase 1 or 2.

Inclusion Criteria:

• Phase 1 Part: Patients with pathologically confirmed advanced stage B-cell NHL (Ann Arbor stage 3 or 4) for whom R-CHOP is considered appropriate therapy; newly diagnosed DLBCL, newly diagnosed low grade B cell NHL, and previously treated low grade B cell NHL patients in first relapse after a prior treatment with non-anthracycline containing chemotherapy are allowed; double hit and transformed diffuse large B cell lymphoma are allowed

  * Allowed low grade B cell lymphomas will include follicular lymphoma any grade, marginal zone lymphoma including mucosa-associated lymphoid tissue (MALT) lymphoma, indolent mantle cell lymphoma and Waldenstrom's macroglobulinemia

• Phase 2 Part: Patients with pathologically confirmed newly diagnosed diffuse large B cell lymphoma (Ann Arbor stage 3 or 4); newly diagnosed double hit and transformed diffuse large B cell lymphoma are allowed

• Patients must have measurable disease, defined as at least one lesion above and below the diaphragm or stage 4 disease that can be accurately measured in at least one dimension; lymph nodes should be considered abnormal if the long axis is > 1.5 cm, regardless of the short axis

• Allowed prior therapy:

  • Newly diagnosed DLBCL and low grade B cell lymphoma: No prior therapy is allowed except steroids equivalent to maximum of prednisone 20 mg once daily for maximum of seven days prior to registration
  • Relapsed/refractory low grade B cell lymphoma (only allowed in phase I): A minimum and maximum of one line of prior non-anthracycline containing therapy is allowed; prior localized radiation therapy is not considered a line
  • For patients who have had prior chemotherapy or immunotherapy, at least 2 weeks must have elapsed between last dose and initial dose of RCHOP-selinexor; for patients treated with radio-immunotherapy, at least 12 weeks

• All races and ethnic groups are eligible for this trial

• Eastern Cooperative Oncology Group (ECOG) performance status =< 1 (Karnofsky >= 60%)

• Life expectancy of greater than 6 months

• Premenopausal female patients of child-bearing potential must agree to use dual methods of contraception and have a negative serum pregnancy test at screening, and male patients must use an effective barrier method of contraception if sexually active with a female of child-bearing potential; acceptable methods of contraception are condoms with contraceptive foam, oral, implantable or injectable contraceptives, contraceptive patch, intrauterine device, diaphragm with spermicidal gel, or a sexual partner who is surgically sterilized or post-menopausal; for both male and female patients, effective methods of contraception must be used throughout the study and for three months following the last dose

• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Patients with DLBCL who have received chemotherapy or immunotherapy (except one week of steroids as described above) at any time point in the past for therapy of the DLBCL; patients with low grade B cell lymphomas who have received more than one prior line of chemotherapy or any anthracycline-containing therapy in the past for their low grade B cell lymphoma; localized radiation therapy does not count as a line of therapy
• Patients who are receiving any other investigational agents
• Patients with known brain metastases are excluded
• History of severe allergic reactions (as determined by treating physician) attributed to the drugs being used in the study
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, congestive heart failure (New York Heart Association [NYHA] class >= 3 or left ventricular ejection fraction < 45%), unstable angina pectoris, myocardial infarction within the last 3 months, clinically significant cardiac arrhythmia (i.e., ventricular tachycardia on anti-arrhythmia are excluded; 1st degree atrioventricular [AV] block or asymptomatic left anterior fascicular block [LAFB]/right bundle branch block [RBBB] permissible), or psychiatric illness/social situations that would limit compliance with study requirements
• Pregnant and lactating women are excluded
• Human immunodeficiency virus (HIV)-positive patients regardless of treatment are excluded; patients with evidence of active hepatitis B and hepatitis C infection with positive real time polymerase chain reaction (qPCR) are also excluded but patients with prior exposure to hepatitis B or C with negative qPCR are allowed
• Patients with severe intolerance to glucocorticoids
• Major surgery within 2 weeks of first dose of study drug
• Patients who are unable to swallow tablets, patients with malabsorption syndrome, or any other gastrointestinal (GI) disease or GI dysfunction that could interfere with absorption of study treatment
• Absolute neutrophil count (ANC) < 1500 cells/mm^3
• Platelet count < 100,000/mm^3
• Serum bilirubin > 1.5 times the upper limit of normal (ULN) (except patients with Gilbert's syndrome: total bilirubin of > 3 x ULN)
• Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) > 2.5 times ULN
• Estimated creatinine clearance of < 30 mL/min, calculated using the formula of Cockroft and Gault