Summary: A 3-dimensional Lie algebra \(s\mu (3)\) is obtained with the help of the known Lie algebra. Based on the \(s\mu (3)\), a new discrete \(3 \times 3\) matrix spectral problem with three potentials is constructed. In virtue of discrete zero curvature equations, a new matrix Lax representation for the hierarchy of the discrete lattice soliton equations is acquired. It is shown that the hierarchy possesses a Hamiltonian operator and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals.