Ribociclib and Gemcitabine Hydrochloride in Treating Patients With Advanced Solid Tumors or Lymphoma

Inclusion Criteria: * Patients must have advanced/metastatic solid malignancy or lymphoma for which no standard treatment option exists that will confer clinical benefit * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Patients enrolled in the dose expansion phase must have at least one measurable lesion as defined by Response Evaluation Criteria in Solid Tumors (RECIST) criteria for solid tumors or measurable nodal disease at baseline as defined by Cheson criteria for lymphoma * Written informed consent must be obtained prior to any screening procedures and according to local guidelines * Life expectancy of \>= 12 weeks * Absolute neutrophil count \>= 1.5 × 10\^9/L * Platelets \>= 100 × 10\^9/L * Hemoglobin \>= 9 g/dL * Potassium above lower limit normal range for the institution; supplementation may be given before the first dose of study medication * Total calcium (corrected for serum albumin if albumin abnormal) above lower limit normal range for the institution; supplementation may be given before the first dose of study medication * Magnesium above lower limit normal range for the institution; supplementation may be given before the first dose of study medication * Sodium above lower limit normal range for the institution; supplementation may be given before the first dose of study medication * Phosphorus above lower limit normal range for the institution; supplementation may be given before the first dose of study medication * International normalized ratio (INR) =\< 1.5 * Serum creatinine =\< 1.5 mg/dL or creatinine clearance \>= 50 mL/min (calculated by Cockcroft Gault equation) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 upper limit of normal (ULN) or =\< 5 x ULN if liver metastases are present * Total bilirubin =\< ULN; or total bilirubin =\< 3.0 x ULN with direct bilirubin =\< 1.5 ULN n patients with well documented Gilbert's syndrome * Women of childbearing potential must have a negative pregnancy test performed within 7 days prior to the start of study drug * Must be able to swallow ribociclib capsules Exclusion Criteria: * Previous anti-cancer chemotherapy, immunotherapy or investigational agents \< 4 weeks prior to the first day of study defined treatment * Patient who has received radiotherapy =\< 4 weeks or limited field radiation for palliation =\< 2 weeks prior to starting study drug, and who has not recovered to grade 1 or better from related side effects of such therapy (exceptions include alopecia) and/or in whom \>= 25% of the bone marrow was irradiated * Patient has had major surgery within 14 days prior to starting study drug or has not recovered from major side effects (tumor biopsy is not considered as major surgery) * Active clinically serious infections or other serious uncontrolled medical conditions * Patient has impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection) * Patient has baseline neuropathy of \> grade 2 * Patient has known hypersensitivity to any of the excipients of ribociclib * Patient has a known history of human immunodeficiency virus (HIV) infection (testing not mandatory) * Patients with central nervous system (CNS) involvement unless they meet ALL of the following criteria: * At least 4 weeks from prior therapy completion (including radiation and/or surgery) to starting the study treatment * Clinically stable CNS tumor at the time of screening and not receiving steroids and/or enzyme-inducing anti-epileptic medications for brain metastases * Clinically significant, uncontrolled heart disease and/ or a history of cardiac dysfunction including any of the following: * History of unstable angina pectoris, symptomatic pericarditis, myocardial infarction, coronary artery bypass grafting or coronary angioplasty within 12 months prior to study entry * History of documented congestive heart failure (New York Heart Association functional classification III-IV) * Documented cardiomyopathy * Patient has a left ventricular ejection fraction (LVEF) \< 50% as determined by multiple gated acquisition (MUGA) scan or echocardiogram (ECHO) * History of clinically significant ventricular arrhythmia and/or conduction delays within 12 months of screening * Systolic blood pressure \> 160 mmHg or \< 90 mmHg * Congenital long QT syndrome or family history of long QT syndrome * Bradycardia (heart rate \< 50 at rest) by electrocardiogram (ECG) or pulse at screening. * On screening, inability to determine the Fridericia corrected QT interval (QTcF) interval on the ECG (i.e.: unreadable or not interpretable) or QTcF \> 450 msec (using Fridericia's correction); all as determined by screening ECG (mean of triplicate ECGs) * Patient has any other concurrent severe and/or uncontrolled medical condition that would, in the investigator's judgment, cause unacceptable safety risks, contraindicate patient participation in the clinical study or compromise compliance with the protocol (e.g., chronic pancreatitis, chronic active hepatitis, active untreated or uncontrolled fungal, bacterial, or viral infections etc.) * Patient is currently receiving any of the following medications and cannot be discontinued 7 days prior to starting study drug (for details): * Known strong inducers or inhibitors of cytochrome P450, family 3, subfamily A, polypeptide 4/5 (CYP3A4/5) including grapefruit, grapefruit hybrids, pummelos, star-fruit, and Seville oranges * Those have a narrow therapeutic window and are predominantly metabolized through CYP3A4 * Those have a known strong risk to prolong the QT interval or induce Torsades de Pointes * Herbal preparations * Patient is currently receiving or has received systemic corticosteroids (=\< 2 weeks prior to starting study drug, or who have not fully recovered from side effects of such treatment) * The following uses of corticosteroids are permitted: single doses, topical applications (e.g., for rash), inhaled sprays (e.g., for obstructive airways diseases), eye drops or local injections (e.g., intra-articular) * Patient has a history of non-compliance to medical regimen or inability to grant consent * Patient is currently receiving warfarin or other coumarin-derived anticoagulant for treatment, prophylaxis or otherwise; therapy with heparin, low molecular weight heparin (LMWH) or fondaparinux is allowed * Participation in a prior investigational study within 30 days prior to enrollment or within 5 half-lives of the investigational product, whichever is longer * Patient has not recovered from all toxicities related to prior anticancer therapies to grade 1 per National Cancer Institute (NCI)-Common Terminology Criteria for Adverse Events (CTCAE) version 4.03 (exception to this criterion: patients with any grade of alopecia are allowed to enter the study) * Patient with a Child-Pugh score B or C (for cirrhosis patients only) * Pregnant or nursing (lactating) women, where pregnancy is defined as the state of a female after conception and until the termination of gestation, confirmed by a positive human chorionic gonadotropin (hCG) laboratory test * Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, unless they are using highly effective methods of contraception throughout the study and for 8 weeks after study drug discontinuation; highly effective contraception methods include: * Total abstinence when this is in line with the preferred and usual lifestyle of the patient; periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy) or tubal ligation at least 6 weeks before taking study treatment; in case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment * Male sterilization (at least 6 months prior to screening); for female patients on the study, the vasectomized male partner should be the sole partner for that patient * Combination of any of the 2 following (a+b or a+c or b+c) * a. Use of oral, injected or implanted hormonal methods of contraception or other forms of hormonal contraception that have comparable efficacy (failure rate \< 1%), for example hormone vaginal ring or transdermal hormone contraception * b. Placement of an intrauterine device (IUD) or intrauterine system (IUS) * c. Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/ vaginal suppository * In case of use of oral contraception, women should have been stable on the same pill before taking study treatment * Note: oral contraceptives are allowed but should be used in conjunction with a barrier method of contraception * Women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago; in the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential * Sexually active males unless they use a condom during intercourse while taking the drug and for 21 days after stopping treatment and should not father a child in this period; a condom is required to be used also by vasectomized men