Entospletinib and Obinutuzumab in Treating Patients With Relapsed Chronic Lymphocytic Leukemia, Small Lymphocytic Lymphoma, or Non-Hodgkin Lymphoma

Inclusion Criteria: * Phase I portion of the study: Histologically or flow cytometry confirmed diagnosis of B-CLL/SLL according to National Cancer Institute (NCI)-Working Group (WG) 1996 guidelines * Phase I portion of the study: The following types of NHL as documented by medical records and with histology based on criteria established by the World Health Organization (WHO): * Mantle cell lymphoma (MCL) * Follicular lymphoma (FL) - grades 1-3a * Lymphoplasmacytic lymphoma (LPL) * Marginal zone lymphoma (MZL) * CLL in Richter's transformation * B-cell prolymphocytic leukemia * Phase I portion of the study: Patients with histologically confirmed classical hairy cell leukemia (HCL) * Phase II portion of the study - histologically or flow cytometry confirmed diagnosis of BCLL/SLL according to NCI-WG 1996 guidelines; patients who lack CD23 expression on their leukemia cells should be examined for (and found NOT to have) either t(11;14) or cyclin D1 overexpression, to rule out mantle cell lymphoma * Patients underwent \>= 1 prior chemotherapy-based or immunotherapy-based regimen or targeted therapy (e.g., inhibitors of BTK, PI3K etc.) administered for \>= 2 cycles, and have had either documented disease progression or no response (stable disease) to the most recent treatment regimen * Patients with CLL/SLL must demonstrate active disease meeting at least 1 of the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria for requiring treatment: * A minimum of any one of the following constitutional symptoms: * Unintentional weight loss \> 10% within the previous 6 months prior to screening * Extreme fatigue (unable to work or perform usual activities) * Fevers of greater than 100.5 Fahrenheit (F) for \>= 2 weeks without evidence of infection * Night sweats without evidence of infection * Evidence of progressive marrow failure as manifested by the development of, or worsening of anemia or thrombocytopenia * Massive (i.e., \> 6 cm below the left costal margin), progressive or symptomatic splenomegaly * Massive nodes or clusters (i.e., \> 10 cm in longest diameter) or progressive lymphadenopathy * Progressive lymphocytosis with an increase of \> 50% over a 2-month period, or an anticipated doubling time of less than 6 months * Autoimmune anemia or thrombocytopenia that is poorly responsive to corticosteroids * Patients with HCL must be intolerant of or not candidates for purine analog-based therapy, or failed to achieve response (CR or partial response \[PR\]) or relapsed within 2 years of such therapy, AND meet the standard treatment initiation criteria (absolute neutrophil count \[ANC\] =\< 1000/uL, hemoglobin \[Hgb\] =\< 10 g/dL, platelet count =\< 100,000/uL); patients with indolent lymphoma (FL, LPL, MZL) and patients with B-cell prolymphocytic leukemia must have an indication for treatment in the opinion of the investigator; patients with MCL and patients with CLL in Richter's transformation should have previously received or not be candidates for high dose chemotherapy/autologous stem cell transplant * For diseases other than CLL, LPL, and HCL, presence of radiographically measurable lymphadenopathy or extra-nodal lymphoid malignancy (defined as the presence of \>= 1 lesion that measures \>= 2.0 cm in the longest dimension \[LD\] and \>= 1.0 cm in the longest perpendicular dimension \[LPD\] as assessed by computed tomography \[CT\] or magnetic resonance imaging \[MRI\]); for LPL, measurable disease will be defined as serum monoclonal IgM \> 0.5 g/dL or meeting at least 1 of the recommendations from the Second International Workshop on LPL for requiring treatment * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Direct bilirubin =\< 2 X institutional upper limit of normal (ULN) (unless due to known Gilbert's syndrome or compensated hemolysis directly attributable to CLL) * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) less than 2.5 X institutional ULN * Estimated creatinine clearance (CrCL) using the Cockcroft-Gault equation \>= 50 mL/min * Platelets \>= 50,000/mm\^3 independent of transfusion support, with no active bleeding * Absolute neutrophil count (ANC) \>= 1000/mm\^3, unless due to disease involvement in the bone marrow * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Prior therapeutic intervention with any of the following: * Therapeutic anticancer antibodies within 4 weeks (rituximab), except within 6 months for obinutuzumab or a similar investigational type II monoclonal antibody; * Radio- or toxin-immunoconjugates within 10 weeks; * Inhibitors of BTK (ibrutinib), PI-3K (idelalisib), BH3-mimetic venetoclax, lenalidomide and other "targeted" therapy (including but not limited to investigational BTK and PI-3K inhibitors, etc.) - within 6 half-lives (i.e., 36 hours for ibrutinib) * All other chemotherapy, radiation therapy within 3 weeks prior to initiation of therapy * SYK inhibitors at any time * Inadequate recovery from adverse events related to prior therapy to grade =\< 1 (excluding grade 2 alopecia and neuropathy) * Chronic use of corticosteroids in excess of prednisone 30 mg/day or its equivalent * Stem cell transplant recipients must have no evidence of and not receive treatment for graft-versus-host disease * Concomitant use or use in the prior two weeks of moderate or strong CYP3A and CYP2C9 inducers or strong CYP2C9 inhibitors, including nutraceutical preparations, e.g., grapefruit juice and St John's wort * History prior malignancy except: * Malignancy treated with curative intent and no known active disease present for \>= 2 years prior to initiation of therapy on current study * Adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease * Adequately treated in situ carcinomas (e.g., cervical, esophageal, etc.) without evidence of disease * Asymptomatic prostate cancer managed with "watch and wait" strategy * Myelodysplastic syndrome which is clinically well controlled and no evidence of the cytogenetic abnormalities characteristic of myelodysplasia on the bone marrow at screening * Uncontrolled immune hemolysis or thrombocytopenia (positive direct antiglobulin test in absence of hemolysis or history of immune-mediated cytopenias are not exclusions) * History of human immunodeficiency virus (HIV) infection or active hepatitis B or C * Major surgery (requiring general anesthesia) within 2 weeks prior to initiation of therapy * Inability to swallow and retain an oral medication; patients with clinically significant medical condition of malabsorption, inflammatory bowel disease, chronic conditions which manifest with diarrhea, refractory nausea, vomiting or any other condition that will interfere significantly with drug absorption are excluded; patients must also have adequate venous access * Need for ongoing therapy with proton pump inhibitors; H2 antagonists are allowed * Active uncontrolled infection * Women who are pregnant or lactating * Fertile men or women of childbearing potential unless 1) permanently sterile or 2) using a highly effective measure of contraception such as condoms in males and consistent and correct use of one of the following in females: intrauterine device, tubal sterilization, Essure micro-insert system, vasectomy in the male partner; effective contraception is required for males during treatment with study drug and to continue for 3 months after the last dose of either entospletinib or obinutuzumab, whichever is later; for women, effective contraception is required to continue for 18 months after the last dose of obinutuzumab or for 30 days after the last dose of entospletinib, whichever is later * Definition of childbearing potential: for this study, a female subject is considered of childbearing potential until becoming post-menopausal unless permanently sterile or with medically documented ovarian failure; women are considered to be in a postmenopausal state when \>= 54 years of age with cessation of previously occurring menses for \>= 12 months without an alternative cause; women of any age with amenorrhea of \>= 12 months may also be considered post-menopausal if their follicle stimulating hormone (FSH) level is in the post-menopausal range and they are not using hormonal contraception or hormonal replacement therapy; permanent sterilization in females includes hysterectomy, bilateral oophorectomy, or bilateral salpingectomy in a female subject of any age; permanent sterilization in males include bilateral orchiectomy or medical documentation of alternative explanation * Any condition for which participation in the study is judged by the Investigator to be detrimental to the patient with inter-current illness or psychiatric/social situations that would jeopardize compliance with study requirements