We employ variational and diffusion Monte Carlo methods to calculate. the ground state properties of both pure and Li doped solid Hz. The absorption spectra of Li in the H-2 solid are calculated from the sampled ground state configurations and a pseudothermal semiclassical spectral line theory, based on the Franck-Condon principle for a condensed phase system. The T=O numerical results of various thermodynamic properties of the pure and doped solid agree well with those from. previous theoretical calculations. However, the Li spectra differ significantly from results of a finite temperature path integral Monte Carlo calculation [D. Scharf et al., J. Chem. Phys. 99, 9013 (1993)], which employed a different Li*-H-2 potential. The differences in two calculations are extensively discussed here, and comparisons are also made with available experimental data. We demonstrate that accurate measurements of the Li absorption spectrum provide a powerful means to probe the local structures of the Li trapping sites.