Let ℒ 1 and ℒ 2 be lattices of subsets of a nonempty set X . Suppose ℒ 2 coallocates ℒ 1 and ℒ 1 is a subset of ℒ 2 . We show that any ℒ 1 -regular finitely additive measure on the algebra generated by ℒ 1 can be uniquely extended to an ℒ 2 -regular measure on the algebra generated by ℒ 2 . The case when ℒ 1 is not necessary contained in ℒ 2 , as well as the measure enlargement problem are considered. Furthermore, some discussions on normal lattices and separation of lattices are also given.