In this paper, we introduced Smarandache-2-algebraic structure of Lattice. A Smarandache-2-algebraic structure on a set N means a weak algebraic structure S1 on N such that there exist a proper subset M of N, which is embedded with a stronger algebraic structure S2, stronger algebraic structure means satisfying more axioms, that is S1<<S2, by proper subset one can understand a subset different from the empty set, from the unit element if any, from the whole set. We define Smarandache-Lattice and construct its algorithms through orthomodular lattice, residuated lattice,pseudocomplment lattice, arbitrary lattice and congruence and ideal

lattice.