Phase transitions of cellular proteins and lipids play a key role in governing the organisation and coordination of intracellular biology. The frequent juxtaposition of proteinaceous biomolecular condensates to cellular membranes raises the intriguing prospect that phase transitions in proteins and lipids could be co-regulated. Here we investigate this possibility in the ribonucleoprotein (RNP) granule-ANXA11-lysosome ensemble, where ANXA11 tethers RNP granule condensates to lysosomal membranes to enable their co-trafficking. We show that changes to the protein phase state within this system, driven by the low complexity ANXA11 N-terminus, induce a coupled phase state change in the lipids of the underlying membrane. We identify the ANXA11 interacting proteins ALG2 and CALC as potent regulators of ANXA11-based phase coupling and demonstrate their influence on the nanomechanical properties of the ANXA11-lysosome ensemble and its capacity to engage RNP granules. The phenomenon of protein-lipid phase coupling we observe within this system offers an important template to understand the numerous other examples across the cell whereby biomolecular condensates closely juxtapose cell membranes.