Extensive molecular dynamics simulations have been carried out to calculate the orientational correlation functions C-l(t), C-l(t) = [4 pi/(2l + 1)]Sigma(m=-l)(l) [Y*(lm)(Omega(0)) Y-lm(Omega(t))] (where Y-lm(Omega) are the spherical harmonics) of point dipoles in a cubic lattice. The decay of C-1(t) is found to be strikingly different from higher l-correlation functions-the latter do not exhibit diffusive dynamics even in the long time. Both the cumulant expansion expression of Lynden-Bell and the conventional memory function equation provide very good description of the C-1(t) in the short time but fail to reproduce the observed slow, long time decay of C-1(t).