Based on the weight and dosage provided (40 lbs and 15 mg/week), the child is currently receiving more than 0.4 mg/kg/week of methotrexate. This meets the Infectious Disease Society of America (IDSA) definition of high-level immunosuppression. Administration of both varicella and MMR vaccines are contraindicated until such time as the methotrexate dosage can be reduced. The 2013 IDSA definition of low-level immunosuppression for methotrexate is a dosage of less than 0.4 mg/kg/week. For additional details, see the 2013 IDSA Clinical Practice Guideline for Vaccination of the Immunocompromised Host: cid.oxfordjournals.org/content/early/2013/11/26/cid.cit684.full.pdf.
As a general rule, whenever feasible, it is recommended that non-live and live vaccines be administered 2 or more weeks before initiating immunosuppressive medications include human immune mediators like interleukins and colony-stimulating factors, immune modulators, and medicines like tumor necrosis factor-alpha inhibitors and anti-B cell agents. See CDC General Best Practice Guidelines for Immunization section on altered immunocompetence: www.cdc.gov/vaccines/hcp/acip-recs/general-recs/immunocompetence.html.