We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients η and ζ of the membrane fluid. We show that the membrane pressure is intimately connected with Noether charge entropy S Wald of the horizon when we consider a specific m-th order Lanczos Lovelock model, through the relation p (m)A/T = [(D - 2m)/(D - 2)] S Wald (m), where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons. The bulk and shear viscosity coefficients are found to obey the relation ζ = -2(D - 3)/(D - 2)η. © 2012 SISSA.