The regulation of gene expression is governed at multiple levels of chromatin organization. However, how coordination is achieved remains relatively unexplored. Here we present Dam&ChIC, a method that enables time-resolved and multifactorial chromatin profiling at high resolution in single cells. Analysis of genome-lamina interactions in haploid cells reveals highly dynamic spatial repositioning of small domains during interphase and partial inheritance over mitosis. Dam&ChIC applied to study random X-inactivation uncovers that spreading of H3K27me3 on the inactive X chromosome (Xi) overlaps with remarkable genome-lamina detachment. We find that genome-lamina detachment precedes H3K27me3 accumulation on the Xi and occurs upon mitotic exit. Domains that retain genome-lamina interactions are marked by high pre-existing H3K9me3 levels. These findings imply an important role for genome-lamina interactions in regulating H3K27me3 accumulation on the Xi. We anticipate that Dam&ChIC will be instrumental in unraveling the interconnectivity and order of chromatin events underlying cell-state changes in single cells.