Efimov's effect for a system of three particles moving on three-dimensional lattice and interacting via pairwise short-range potentials is studied. The following new results will be presented: (i). Infinitude of the number of eigenvalues (Efimov's effect) for zero quasi-momentum, and its finiteness for non-zero values of the quasi-momentum. (ii).The corresponding asymptotics for the number of eigenvalues.