This phase II trial studies how well ibrutinib, fludarabine phosphate, cyclophosphamide, and obinutuzumab work in treating patients with chronic lymphocytic leukemia. Ibrutinib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as fludarabine phosphate and cyclophosphamide, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Immunotherapy with monoclonal antibodies, such as obinutuzumab, may induce changes in the body's immune system and may interfere with the ability of tumor cells to grow and spread. Giving ibrutinib, fludarabine phosphate, cyclophosphamide, and obinutuzumab together may work better in treating chronic lymphocytic leukemia.

PRIMARY OBJECTIVE:

I. Estimate therapeutic activity (achievement of complete remission [CR] or CR with incomplete marrow recovery [CRi] and bone marrow minimal residual disease [MRD] negativity after 3 courses) of first-line treatment with ibrutinib, fludarabine (fludarabine phosphate), cyclophosphamide, obinutuzumab (GA101) (iFCG) in patients with chronic lymphocytic leukemia (CLL) who have mutated immunoglobulin heavy chain variable region (IGHV) and non-del(chromosome 7, p arm [17p]) fluorescence in-situ hybridization (FISH).

SECONDARY OBJECTIVES:

I. Estimate the rate of conversion of bone marrow MRD-positive after 3 courses of iFCG to bone marrow MRD-negative with 9 additional courses of ibrutinib and obinutuzumab (iG).

II. Determine the safety of this combination in the proposed patient population.

III. Determine the progression-free survival (PFS). IV. Determine the overall survival (OS). V. Determine the long-term incidence of secondary myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML), and Richter's transformation.

VI. Perform ribonucleic acid (RNA) profiling to identify molecules responsible for response and/or relapse.

VII. Investigate impact on breakpoint cluster region (BCR) pathway and deoxyribonucleic acid (DNA) damage response pathway proteins during therapy.

OUTLINE:

INDUCTION CYCLE 1: Patients receive obinutuzumab intravenously (IV) over 4-6 hours on days 1, 2, 8 and 15, fludarabine phosphate IV over 15 minutes and cyclophosphamide IV over 30 minutes on days 2-4. Patients also receive ibrutinib orally (PO) once daily (QD) on days 1-28.

INDUCTION CYCLES 2 and 3: Patients receive obinutuzumab IV over 4-6 hours on day 1, fludarabine phosphate IV over 15 minutes and cyclophosphamide IV over 30 minutes on days 1-3. Patients also receive ibrutinib PO QD on days 1-28.

MAINTENANCE: Patients receive 1 of 5 maintenance regimens as determined by disease status.

REGIMEN I CYCLES 4 and 6: Patients achieving CR/CRi and bone marrow MRD-negative receive maintenance therapy comprising obinutuzumab IV over 4-6 hours on day 1, and ibrutinib PO QD on days 1-28. Treatment repeats every 28 days for up to 3 cycles in the absence of disease progression or unacceptable toxicity.

REGIMEN I CYCLES 7 and 12: Patients remaining bone marrow MRD-negative receive maintenance therapy comprising ibrutinib PO QD on days 1-28. Treatment repeats every 28 days for up to 6 cycles in the absence of disease progression or unacceptable toxicity.

REGIMEN I CYCLES 7 and 12: Patients converting bone marrow MRD-positive receive maintenance therapy comprising obinutuzumab IV over 4-6 hours on day 1, and ibrutinib PO QD on days 1-28. Treatment repeats every 28 days for up to 6 cycles in the absence of disease progression or unacceptable toxicity.

REGIMEN II CYCLES 4 and 12: Patients achieving less than CR/CRi and/or bone marrow MRD-positive receive maintenance therapy comprising obinutuzumab IV over 4-6 hours on day 1, and ibrutinib PO QD on days 1-28. Treatment repeats every 28 days for up to 9 cycles in the absence of disease progression or unacceptable toxicity.

REGIMEN II AFTER 12 CYCLES: Patients still bone marrow MRD-positive receive maintenance therapy comprising ibrutinib PO QD on days 1-28. Treatment repeats every 28 days in the absence of disease progression or unacceptable toxicity.

Inclusion Criteria:

• Patients with a diagnosis of CLL/small lymphocytic lymphoma (SLL), with mutated (> 2% deviation from germ line) IGHV gene, who meet criteria to initiate first-line treatment per International Workshop on CLL Working Group (IWCLL) 2008 guidelines
• Patients must not have received prior CLL-directed therapy
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2
• Absolute neutrophil count > 500 uL
• Platelet count > 50,000/uL
• Serum total bilirubin =< 1.5 x upper limit of normal (ULN) or =< 3 x ULN for patients with Gilbert's disease
• Estimated creatinine clearance >= 30 mL/min (calculated or measured by 24 hour urine collection)
• Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 2.5 x ULN
• Women of childbearing potential must have a negative serum or urine beta human chorionic gonadotropin (beta-hCG) pregnancy test result within 14 days prior to the first dose of study drugs and must agree to use an effective contraception method during the study and for 30 days following the last dose of study drug; women of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy; men who have partners of childbearing potential must agree to use an effective contraceptive method during the study and for 30 days following the last dose of study drug
• Free of prior malignancies for 3 years with exception of patients diagnosed with basal cell or squamous cell carcinoma of the skin, or carcinoma "in situ" of the cervix or breast, who are eligible even if they are currently treated or have been treated and/or diagnosed in the past 2 years prior to study enrollment; if patients have another malignancy that was treated within the last 2 years, such patients can be enrolled, after consultation with the principal investigator, if the likelihood of requiring systemic therapy for this other malignancy within 2 years is less than 10%, as determined by an expert in that particular malignancy at MD Anderson Cancer Center
• Patients or their legally authorized representative must provide written informed consent
• Prothrombin time (PT)/international normalization ratio (INR) < 1.5 x ULN
• Partial thromboplastin time (PTT) < 1.5 x ULN
• Activated partial thromboplastin time (aPTT) < 1.5 x ULN

Exclusion Criteria:

• Major surgery, radiotherapy, chemotherapy, biologic therapy, immunotherapy, experimental therapy within 3 weeks prior to the first dose of the study drugs and/or monoclonal antibody =< 6 weeks prior to first administration of study treatment
• Patients with del(17p) by FISH (or known tumor protein p53 [TP53] mutation)
• Patients with unmutated (=< 2% homology with germ line) IGHV
• Uncontrolled active systemic infection (viral, bacterial, and fungal)
• Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, QT prolongation or familial history of QT prolongation, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification
• History of stroke or cerebral hemorrhage within 6 months
• Patient is pregnant or breast-feeding
• Current or chronic hepatitis B or C infection, or known seropositivity for human immunodeficiency virus (HIV); subjects who are positive for hepatitis B or C core antibody or hepatitis B or C surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; Note: Patients who are receiving intravenous immunoglobulins may become seropositive for hepatitis B antibodies; these patients are allowed on the study without additional testing
• Active, uncontrolled autoimmune phenomenon (autoimmune hemolytic anemia or immune thrombocytopenia) requiring steroid therapy
• Concurrent use of investigational therapeutic agent
• Patients may not receive other concurrent chemotherapy, radiotherapy, or immunotherapy; localized radiotherapy to an area not compromising bone marrow function does not apply
• Malabsorption syndrome or other condition that precludes enteral route of administration
• Concomitant use of warfarin or other vitamin K antagonists
• Requires treatment with a strong cytochrome P450 (CYP), family 3, subfamily A (3A) inhibitor
• Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that in the opinion of the investigator may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and/or would make the patient inappropriate for enrollment into this study
• Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia