The 3D organization of the genome changes concomitantly with expression changes during hematopoiesis and immune activation. Studies have focused either on lamina-associated domains (LADs) or on topologically associated domains (TADs), defined by preferential local chromatin interactions, and chromosome compartments, defined as higher-order interactions between TADs sharing functionally similar states. However, few studies have investigated how these affect one another. To address this, we mapped LADs using Lamin B1-DamID during Jurkat T-cell activation, finding significant genome reorganization at the nuclear periphery dominated by release of loci frequently important for T-cell function. To assess how these changes at the nuclear periphery influence wider genome organization, our DamID data sets were contrasted with TADs and compartments. Features of specific repositioning events were then tested by fluorescence in situ hybridization during T-cell activation. First, considerable overlap between TADs and LADs was observed with the TAD repositioning as a unit. Second, A1 and A2 subcompartments are segregated in 3D space through differences in proximity to LADs along chromosomes. Third, genes and a putative enhancer in LADs that were released from the periphery during T-cell activation became preferentially associated with A2 subcompartments and were constrained to the relative proximity of the lamina. Thus, lamina associations influence internal nuclear organization, and changes in LADs during T-cell activation may provide an important additional mode of gene regulation.