By considering a discrete isospectral problem, a whole integrable lattice soliton hierarchy is derived. The modified Toda lattice in (2+1)-dimensions is obtained from the integrable positive and negative lattice equations. A direct method of constructing conservation laws for (2+1)-dimensional lattice equations based on associated matrix spectral problems is proposed, by means of which the conservation laws of the (2+1)-dimensional modified Toda lattice are deduced.