Letermovir for the Prevention of Cytomegalovirus Reactivation in Patients With Hematological Malignancies Treated With Alemtuzumab

Inclusion Criteria: * Confirmed diagnosis of T-cell or B-cell prolymphocytic leukemia, chronic lymphocytic leukemia, peripheral T-cell lymphoma, cutaneous T-cell lymphoma, or Sezary syndrome * Intent to treat with alemtuzumab. Monotherapy or combination with chemotherapy is allowed * Confirmed seropositivity for CMV IgG (\>= 0.7 U/mL) within 1 year of first letermovir dose * Confirmed lack of active CMV infection as evidenced by: * Undetectable CMV deoxyribonucleic acid (DNA) by Abbott RealTime CMV in vitro polymerase chain reaction assay (\< 50 IU/mL) within 7 days of first letermovir dose AND * Negative CMV IgM (\< 30 AU/mL) within 7 days of first letermovir dose * Able to provide informed consent * Life expectancy \> 4 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 3 * Highly unlikely to become pregnant or impregnate a partner by meeting at least one of the following: * A female subject who is not of reproductive potential is eligible without requiring the use of contraception. A female subject who is not of reproductive potential is defined as one who: * Has reached natural menopause (defined as 6 months of spontaneous amenorrhea with serum follicle-stimulating hormone \[FSH\] levels in the postmenopausal range as determined by the local laboratory, or 12 months of spontaneous amenorrhea) OR * Is 6 weeks post-surgical bilateral oophorectomy with or without hysterectomy OR * Has undergone bilateral tubal ligation. Spontaneous amenorrhea does not include cases for which there is an underlying disease that causes amenorrhea (e.g., anorexia nervosa) * A male subject who is not of reproductive potential is eligible without requiring the use of contraception. A male subject who is not of reproductive potential is defined as one whom has undergone a successful defined as: * Microscopic documentation of azoospermia OR * A vasectomy more than 2 years ago with no resultant pregnancy despite sexual activity post-vasectomy * A male or female subject who is of reproductive potential agrees to true abstinence or to use (or have their partner use) an acceptable method of birth control starting from the time of consent through 90 days after the last dose of study therapy. True abstinence is defined as abstinence in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., abstinence only on certain calendar days, abstinence only during ovulation period, use of symptothermal method, use of post-ovulation methods) and withdrawal are not acceptable methods of contraception. Acceptable methods of birth control are: * Intrauterine device (IUD), diaphragm with spermicide, contraceptive sponge, condom, and vasectomy OR use of appropriate double barrier contraception. Hormonal contraceptives (e.g., birth control pills, transdermal patch, or injectables) are also acceptable Exclusion Criteria: * History of confirmed CMV disease within 1 year of study entry * History of prior allogeneic hematopoietic stem cell transplant * End stage renal disease with creatinine clearance \< 10 mL/min as defined by Cockcroft-Gault equation using serum creatinine within 7 days of enrollment * Child-Pugh class C within 7 days of enrollment * Serum aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 5 times the upper limit of normal (ULN) or serum total bilirubin \> 2.5 x ULN * Note: Subjects who meet this exclusion criterion may, at the discretion of the investigator, have one repeat testing done. If the repeat value does not meet this criterion, they may continue in the screening process. Only the specific out of range value should be repeated (not the entire panel) * Both moderate hepatic insufficiency AND moderate renal insufficiency: * Moderate hepatic insufficiency is defined as Child Pugh Class B * Moderate renal insufficiency is defined as a creatinine clearance less than 50 mL/min, as calculated by the Cockcroft-Gault equation * Cytopenias are NOT an exclusion criteria in this trial as cytopenias are common in this patient population and letermovir has no known adverse effects on blood counts. Patients will be treated per institutional standard of care with as needed transfusions and growth factor support * Received any of the following drugs within 7 days of enrollment or plans to receive any of the following during the study: * Ganciclovir * Valganciclovir * Foscarnet * Acyclovir (at doses \> 3200 mg PO per day or \> 25 mg/kg IV per day) * Valacyclovir (at doses \> 3000 mg PO per day) * Famciclovir (at doses \> 1500 mg PO per day) * Cyclosporine A * Pimozide * Ergot alkaloids (ergotamine and dihydroergotamine) * Atorvastatin at doses greater than 20 mg daily * Received any of the following within 30 days prior to enrollment * Cidofovir * CMV hyper-immune globulin * Any investigational CMV antiviral agent/biologic therapy * Infection or underlying disease necessitating ongoing use of prohibited medications * Suspected or known hypersensitivity to active or inactive ingredients of letermovir formulations * Positive at the time of screening for: * Human immunodeficiency virus (HIV) with CD4 count \< 350. If HIV positive, must remain on antiretroviral therapy that is not anticipated to interact with letermovir throughout study * Hepatitis B surface antigen or core antibody positivity associated with detectable viral load. For any patient with serologic evidence of prior infection but undetectable viral load, viral load and surface antigen will be monitored every 2 weeks. Those with evidence of reactivation (detectable viral load) will be treated with entecavir or lamivudine. Upon resolution of detectable viral load, the patient will be allowed to continue on trial assuming adequate liver function as defined above. Alternatively, patients may be put on prophylactic entecavir or lamivudine to prevent hepatitis B reactivation at the investigator's discretion * Hepatitis C if no prior or current curative antiviral therapy. For those currently on curative antiviral therapy, they will be allowed on trial if hepatitis C virus (HCV) quantitation is below the limit of detection and adequate liver function as above * Pregnant or expecting to conceive, is breastfeeding, or plans to breastfeed from the time of consent through 90 days after the last dose of study therapy * Expecting to donate eggs or sperm starting from the time of consent through 90 days after the last dose of study therapy * Currently participating or has participated in a study with an unapproved investigational compound or device within 28 days, or 5X half-life of the investigational compound (excluding monoclonal antibodies), whichever is longer, of initial dosing on this study. Subjects previously treated with a monoclonal antibody will be eligible to participate after a 28-day washout period * Previous participation in a study using letermovir * Has a history or current evidence of any condition, therapy, lab abnormality, or other circumstance that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or would be put at undue risk as judged by the investigator, such that it is not in the best interest of the subject to participate in this study