We present a simple model of a membrane bound protein allosterically regulated by the local lipid composition. We are motivated by the experimental finding that the plasma membranes of mammalian cells are tuned close to a liquid-liquid critical point, where the sensitivity of many properties to perturbations is large. We consider a protein whose boundary conditions with the surrounding membrane are dependent on its functional state (i.e. conducting vs. non-conducting for an ion channel). For such a protein we show that small changes in the chemical potential of lipids can lead to dramatic functional changes near a critical point. This type of regulation becomes more potent as the protein becomes larger, and as the membrane gets closer to a critical point. Such a protein would also have its nanometer-scale localization correlated with its functional state. A cell could regulate such a protein by adjusting the composition either by changing the ratio of ordered to disordered lipids (experimentally probed by cholesterol depletion and loading) or by raising or lowering the critical temperature. Here we focus on perturbations that act to lower the critical temperature, like the liquid general anesthetics that have been shown to lower critical temperatures by ∼4K at clinically relevant concentrations. We show that this change is sufficient to lead to changes in channel conductivity in line with what has been shown for a wide class of channels even without specific interactions between perturbing molecules and the channel itself.