Hutchinson–Gilford progeria syndrome (HGPS) is a rare genetic disease that causes premature aging symptoms, such as vascular diseases, lipodystrophy, loss of bone mineral density, and alopecia. HGPS is mostly linked to a heterozygous and de novo mutation in the LMNA gene (c.1824 C > T; p.G608G), resulting in the production of a truncated prelamin A protein called “progerin”. Progerin accumulation causes nuclear dysfunction, premature senescence, and apoptosis. Here, we examined the effects of baricitinib (Bar), an FDA-approved JAK/STAT inhibitor, and a combination of Bar and lonafarnib (FTI) treatment on adipogenesis using skin-derived precursors (SKPs). We analyzed the effect of these treatments on the differentiation potential of SKPs isolated from pre-established human primary fibroblast cultures. Compared to mock-treated HGPS SKPs, Bar and Bar + FTI treatments improved the differentiation of HGPS SKPs into adipocytes and lipid droplet formation. Similarly, Bar and Bar + FTI treatments improved the differentiation of SKPs derived from patients with two other lipodystrophic diseases: familial partial lipodystrophy type 2 (FPLD2) and mandibuloacral dysplasia type B (MADB). Overall, the results show that Bar treatment improves adipogenesis and lipid droplet formation in HGPS, FPLD2, and MADB, indicating that Bar + FTI treatment might further ameliorate HGPS pathologies compared to lonafarnib treatment alone.