Hutchinson-Gilford progeria (HGPS) is a premature ageing syndrome caused by a mutation in LMNA, resulting in a truncated form of lamin A called progerin. Progerin triggers loss of the heterochromatic marker H3K27me3, and premature senescence, which is prevented by telomerase. However, the mechanism how progerin causes disease remains unclear. Here, we describe an inducible cellular system to model HGPS and find that LAP2α (lamina-associated polypeptide-α) interacts with lamin A, while its interaction with progerin is significantly reduced. Super-resolution microscopy revealed that over 50% of telomeres localize to the lamina and that LAP2α association with telomeres is impaired in HGPS. This impaired interaction is central to HGPS since increasing LAP2α levels rescues progerin-induced proliferation defects and loss of H3K27me3, whereas lowering LAP2 levels exacerbates progerin-induced defects. These findings provide novel insights into the pathophysiology underlying HGPS, and how the nuclear lamina regulates proliferation and chromatin organization.