This paper gives a general framework for analyzing casebased reasoning to represent a lattice-based relation. This is a generalization of our previous work to analyze case-based reasoning over a boolean domain [Satoh98],[Satoh00a] and a tree-structured domain [Satoh00b]. In these work, we use a set-inclusion based similarity which is a generalization of a similarity measure proposed in a legal domain [Ashley90],[Ashley94]. We show representability of a lattice-based relation, approximation method of constructing a minimal casebase to represent a relation and complexity analysis of the method.