Chromatin interacts with the nuclear lamina, a meshwork of A- and B-type lamins at the nuclear envelope. Interactions of chromatin with the nuclear lamina via lamina-associated domains (LADs) confer structural stability to the genome. However, the dynamics of LAD positioning during differentiation, and how LADs impinge on developmental gene expression, remain elusive. We assessed changes in the association of lamin B1 with the genome in the first 72 h of differentiation of adipose stem cells into adipocytes in vitro. We demonstrate a repositioning of entire stand-alone LADs and of LAD edges (borders) as a prominent nuclear structural feature of early adipogenesis. Whereas adipogenic genes are released from variable LADs (vLADs), vLADs sequester genes involved in non-adipogenic lineages. However, LAD repositioning only partly concurs with gene expression changes, indicating that lamin association is not a primary regulator of lineage-specific gene expression. Further, we identify differentially expressed genes within constitutive LADs (cLADs) during differentiation, which reside in local lamin-depleted and euchromatic “pockets”. In these regions, active histone marks (H3K4me1, H3K4me3 and H3K27ac) before differentiation predict the LAD vs. inter-LAD outcome of these genes after induction of adipogenesis. Differentially expressed genes in LADs are linked to short-range enhancers that in majority co-partition with their cognate genes in LADs and inter-LADs during differentiation. We conclude that LADs and focal euchromatic sites within LADs emerge as determinative structural features of adipose nuclear architecture.