Real cells and many artificial cells are bound by a lipid bilayer membrane as their intrinsic structural matrix. Therefore understanding the interactions between lipid cubic phases and lamellar lipid bilayer structures is fundamental to improving our understanding of drug delivery mechanisms and potential bio-engineering applications within artificial cells. Essential to the functionality of biological membranes is their ability to undergo dynamic shape and topology transformations involved in critical cell activities such as growth, division and trafficking. In nature, a range of protein complexes are involved in the regulation of these membrane remodelling events by a range of active and passive interaction mechanisms that scaffold, bend and cut the membrane as required, including the ESCRTs (endosomal sorting complex required for transport), SNAREs (soluble N-ethylmaleimide-sensitive fusion protein attachment protein receptors), caveolin, dynamin and cytoskeletal filaments. However, the fluidity and flexibility of these interfacial membrane structures are key to these processes and the energy barriers to topological transitions are regulated by lipid composition and the intrinsic curvature stress stored within these membranes, where the shape of lipid molecules influence the lateral stress profile across a bilayer membrane. Therefore seeding lipid bilayer membranes with curved lipid structures such as cubosomes has the potential to enhance their topological activity.