In this paper we introduce and investigate 2-absorbing, n-absorbing, (n, k)-absorbing, weakly 2-absorbing, weakly n-absorbing and weakly (n, k)- absorbing elements in a lattice module M. Some characterizations of 2- absorbing and weakly 2-absorbing elements of M are obtained. By counter example it is shown that a weakly 2-absorbing element of M need not be 2- absorbing. Finally we show that if N ∈ M is a 2-absorbing element, then rad(N) is a 2-absorbing element of M.