This work proves that the process of gluing finite lattices to form a larger lattice is bijective, that is each lattice is the glued sum of a unique system of finite lattices, provided the class of lattices is constrained to modular, locally-finite lattices with finite covers. The results of this work are not surprising given the prior literature, but this seems to be the first proof that the processes of gluing and dissection can be made inverses, and hence that gluing is bijective.