Lower bound approximation and super-convergence of the weak Galerkin spectral element method for second-order elliptic eigenvalue problems are investigated in this talk. At first, we establish the approximation spaces with diverse polynomial degrees of weak functions and weak gradients by using the one-to-one mapping from the reference element to the physical element. Weak Galerkin triangular/quadrilateral spectral element approximation schemes are then proposed for the eigenvalue problem of the second-order elliptic operators. A study on the well-posedness of our schemes is carried out, resulting in the constraint conditions on the polynomial degrees of the discrete weak function space and the discrete weak gradient space. Further, a series of polynomial degree configurations are customized by qualitative numerical analysis such that we obtain the super-convergence of the numerical eigenvalues with the weak Galerkin spectral element method for the first time, and discover some lower bound approximation scenario that has never been reported before in literature. Finally, abundant numerical experiments are reported which verify our theory findings.