A. Czaszar introduced the concept of a semitopogenous order as a binary relation on the power sets of a given set. We extend semitopogenous orders from power sets to arbitrary complete lattices and investigate their behaviour. In particular, we study convergence of generalized nets (upwards closed and centered subsets) with respect to a semitopogenous order and give conditions under which the convergence behaves analogously to the filter convergence in topological spaces. Separation and compactness with respect to a semitopogenous order are discussed, too.