Monte Carlo simulation techniques have been applied to a statistical mechanical lattice model in order to study the coherence length for the spatial fluctuations of the lipid order parameter profiles around integral membrane proteins in dipalmitoyl phosphatidylcholine bilayers. The model, which provides a detailed description of the pure lipid bilayer main transition, incorporates hydrophobic matching between the lipid and protein hydrophobic thicknesses as a major contribution to the lipid-protein interactions in lipid membranes. The model is studied at low protein-to-lipid ratios. The temperature dependence of the coherence length is found to have a dramatic peak at the phase transition temperature. The dependence on protein circumference as well as hydrophobic length is determined and it is concluded that in some cases the coherence length is much longer than previously anticipated. The long coherence length provides a mechanism for indirect lipid-mediated protein-protein long-range attraction and hence plays an important role in regulating protein segregation.