Within the cell, cytoskeletal molecular motors transport and remodel membrane-bound cargos along microtubule and actin filament tracks. Typically, there are multiple actin and microtubule motors attached to the same cargo, which must coordinate to navigate a complex cytoskeletal environment and deliver their cargos to specific locations. We used an engineering, in vitro reconstitution, approach to investigate the interplay between a processive, microtubule-based motor, kinesin-1, and a non-processive, actin filament-based motor, Myo1c, in a simplified environment with increasing physiological complexity. First, we examined the interplay between purified motors attached to a membrane-coated bead at individual actin filament/microtubule intersections on the surface of a coverslip. We found that Myo1c is capable of initiating and terminating microtubule-based, kinesin-1-driven runs at actin filament/microtubule intersections. This ability of Myo1c to affect kinesin-1 motility at actin intersections is inhibited by the presence of nonmuscle tropomyosin Tm2 at the actin intersection. This suggests that tropomyosin may regulate Myo1c tethering of kinesin-1-driven cargo within cells by preventing termination of motility until reaching the highly dynamic actin just beneath the plasma membrane, sorting cargo to distinct subcellular domains. Next, we investigated the interplay between Myo1c and kinesin-1 on deformable giant unilamellar vesicles (GUVs) at physiologically relevant micropatterned arrays of sparse microtubules crossing dense actin filaments. We found that the lipid composition of GUVs regulates its frequency of tubulation along microtubules by kinesin-1 and actin filaments by Myo1c. GUVs containing a PtdIns(4,5)P2-rich lipid composition (PIP2-GUVs) tend to deform at actin/microtubule intersections along the microtubule, yet, the BAR domain protein endophilin is necessary for robust tubulation. Alternatively, in the presence of a physiological lipid mixture (LM-GUVs), kinesin-1 can readily tubulate Myo1c-tethered cargo at actin/microtubule intersections, with no significant change upon addition of endophilin. Myo1c can also transport both PIP2-GUVs and LM-GUVs along actin, yet significantly more deformation and tubulation occurs with LM-GUVs. In both cases, the presence of endophilin increases the frequency of tubulation along actin filaments by Myo1c. Overall, the ability of Myo1c and kinesin-1 to transport, sort, and deform vesicles along microtubules and actin filaments depends on the type of actin track, scaffolding-type membrane deformation-factors like endophilin, and the lipid composition of the vesicle.