We present a thermodynamically consistent coupled PDE system on a closed surface modelling the interplay between lipid raft phase separation and receptor dynamics on a cell membrane. The model is derived via Onsager`s Variational Principle, coupling Cahn-Hilliard equation for lipid ordering to a cross-diffusion system for three receptor states with mixing entropies, volume-filling constraints, and raft-receptor interactions. The system features degenerate mobilities, logarithmic singularities, and equations of mixed second- and fourth-order. Existence of weak solutions is established via techniques from boundedness-by-entropy methods, adapted to the structure and couplings of the system. Uniform energy-entropy estimates are derived to control solutions in appropriate function spaces. At the time-discrete level, auxiliary regularised systems are defined and solved using fixed-point arguments. The entropy variables for the second-order equations are inverted algebraically, while a variational minimisation argument exploits the natural two-sided Flory-Huggins barrier in the fourth-order receptor equation, enforcing strict positivity of receptor fractions. An energy convex splitting is employed for the Cahn-Hilliard equation, giving unconditional stability of the discrete scheme, while the degenerate mobility yields the physically required bound on the order parameter. Compactness arguments allow passage to the limit in approximation parameters, recovering global weak solutions.