This is a two center, 2 arm, Phase II study evaluating the combination of Ribociclib and Everolimus in patients with advanced DDL and LMS who have had at least 1 prior systemic therapy. Patients will be enrolled by sarcoma histology into DDL (Arm A) and LMS (Arm B). The purpose of this study is to determine the anti-tumor activity of this doublet therapy in these patient cohorts. Ribociclib will be administered orally at 300 mg/day 3 weeks on/1 week off. Everolimus will be administered 2.5 mg orally on a continuous 28 day cycle. Clinical and laboratory assessments will be made on day 1, d15 of cycle 1 and 2, and day 1 of each subsequent cycle. Tumor response will be assessed by RECIST 1.1 at (CT or MRI) at week 8, 16, 24 and every 12 weeks thereafter. Study drug administration will continue until disease progression, unacceptable toxicity or withdrawal of consent. Patients will be followed until death or are lost to follow-up for analysis of secondary endpoints.