Triangular norms or t-norm, in short, and automorphisms are very useful to fuzzy logics in the narrow sense. Moreover, these notions are usually limited to the set [0,1]. In this paper we will consider a well known generalization of the t-norm for arbitrary bounded lattices and provide a generalization of automorphism notion for this same structure. We consider several typical lattice constructors and introduce versions of them for t-norms and morphisms. We also analyze some properties of these constructions.