Human Lysozyme Goat Milk for the Prevention of Graft Versus Host Disease in Patients With Blood Cancer Undergoing a Donor Stem Cell Transplant

Inclusion Criteria:

* Documented informed consent of the participant and/or legally authorized representative
* Willingness to be followed for the planned duration of the trial (2 years)
* All subjects must have the ability to understand and the willingness to sign a written informed consent
* Karnofsky performance status \>= 60 per COH SOP
* Patients must be undergoing allogeneic hematopoietic stem cell transplantation (alloHCT) for hematologic malignancies from matched related or matched unrelated donors with 8/8 (A, B, C, DRB 1) high resolution human leukocyte antigen (HLA) donor allele matching
* Patients must be receiving a fractionated total body radiation (FTBI) based- myeloablative conditioning regimen; (acceptable conditioning regimens include total body irradiation \[TBI\] + cyclophosphamide or TBI + etoposide)
* Ejection fraction measured by echocardiogram or multi gated acquisition scan (MUGA) \> 50%
* Diffusing capacity for carbon monoxide (DLCO) adjusted for hemoglobin or forced vital capacity (FVC) \> 50% predicted
* Total serum bilirubin \< 2 times upper limit of normal
* Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) =\< 2.5 x the upper normal limit
* Alkaline phosphatase =\< 2.5 x the upper normal limit
* Measured creatinine clearance more than 60 mL/min
* Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through 90 days after the last dose of protocol therapy

  * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)

Exclusion Criteria:

* Failure of research participant to understand the basic elements of the protocol and/or the risks/benefits of participating in this pilot study. A legal guardian may substitute for the research participant
* Research participants receiving any other investigational agents
* Research participants with presence of other active malignancy within 2 years of study entry. Participants with history of prior malignancy treated with curative intent who achieved complete remission (CR) more than 2 years before study entry are eligible. This exclusion rule does not apply to non-melanoma skin tumors and in-situ cervical cancer
* Research participants having any uncontrolled illness including ongoing or active infection. Research participants with known active hepatitis B or C infection; research participants who are human immunodeficiency virus (HIV) seropositive based on testing performed within 4 weeks of enrollment; research participants with any signs or symptoms of active infection, positive blood cultures, or radiological evidence of infections
* Refusing to use contraception up to 90 days post-HCT
* Pregnant and/or breast feeding if a female recipient
* Lactose intolerance or intolerance to milk products
* In the opinion of the principal investigator (PI), the participant has a condition that will preclude them from complying with study treatment