Lateral force microscopy in the wearless regime was used to study the friction behavior of a lipid monolayer on mica. In the monolayer, condensed domains with long-range orientational order of the lipid molecules were present. The domains revealed unexpectedly strong friction anisotropies and non-negligible friction asymmetries, The angular dependency of these effects correlated well with the tilt direction of the alkyl chains of the monolayer, as determined by electron diffraction and Brewster angle microscopy, The molecular tilt causing these frictional effects was less than 15 degrees, demonstrating that even small molecular tilts can make a major contribution to friction.