Biopolymers that separate into condensed and dilute phases in solution also prewet membranes when one or more components couple to membrane lipids. Here we demonstrate that this prewetting transition becomes exquisitely sensitive to lipid composition when membranes have compositions near the boundary of liquid-ordered/liquid-disordered phase coexistence. In simulation and reconstitution, we couple polyelectrolytes to membranes of saturated lipids, unsaturated lipids, and cholesterol, and find that the coexistence of prewet and dry surface phases is dramatically potentiated by proximity to the membrane phase transition. In cells, we employ an optogenetic tool to characterize prewetting both at the plasma membranes (PM) and the endoplasmic reticulum (ER), and find that prewetting is potentiated or inhibited by perturbations of membrane composition. Prewetting can also mediate membrane adhesion, with avidity dependent on membrane composition. This effect is demonstrated in cells through the potentiation or inhibition of ER-PM contact sites. The strong correspondence between results in simulation, reconstitution, and cells demonstrates a new role for membrane lipids in regulating the recruitment and assembly of soluble proteins.