The cell membrane is a heterogeneously organized composite with lipid-protein micro-domains. The contractile actin cortex may govern the lateral organization of these domains in the cell membrane, yet the underlying mechanisms are not known. We recently reconstituted minimal actin cortices (MACs) (Vogel et al, 2013b) and here introduced phase-separated lipid membranes to the MACs to investigate effects of rearranging actin filaments on the lateral membrane organization. We found that the total contour length of the phase boundary increased upon the addition of actin filaments and reached a steady state where line tension and lateral crowding are balanced. The line tension allows myosin driven actin filament rearrangements to actively move individual lipid domains, often accompanied by their shape change, fusion or splitting. Our findings illustrate how myosin induced actin cortex remodeling in cells may control dynamic rearrangements of lipids and other molecules inside those domains without directly binding to actin filaments.