We report the generation of asymmetric Mathieu optical lattices: invariant intensity optical profiles that
can described by three parameters. The first one describes the amount of ellipticity, the second one
takes into account the degree of asymmetry of the profile, and the third parameter denotes the angular
position where is localized the respective asymmetry. We propose a simple angular spectrum to generate
these nondiffracting beams, and we report how changes their distribution of power and orbital angular
momentum in function of their ellipticity and degree of asymmetry. We confirm the existence of these
invariant beams by propagation in an experimental setup.