In this study, an approximate analytical solution of the Laguerre-Gauss-like vortex solitons was obtained after conducting a second-order perturbation correction in lead glass, a kind of strongly nonlocal nonlinear (1+2)-dimensional medium. Specifically, the nonlocal nonlinear Schr dinger equation (NNLSE) was perturbed using the difference between the real and parabolic refractive indices in lead glass, where the parabolic index was described using the Snyder-Mitchell (SM) model. The Laguerre-Gaussian soliton solution in the SM model is considered to be the ground state solution. Further, the perturbation-corrected Laguerre-Gauss-like solitons with topological charges of 1,2,3, and 4 are more stable when compared to those without perturbation, and their propagation behaviors are almost similar to that of the true soliton solution.