We employ a free energy lattice Boltzmann method to study the dynamics of drops moving across liquid infused surfaces for small but finite contact angles of the lubricant phase. Numerical simulations reveal a rich interplay between contact line pinning and viscous dissipation at the wetting ridge. For low apparent angles, drops move faster with less wetting lubricants, due to the dependence of the lubricant viscous dissipation on the shape of the wetting ridge. In contrast, for large apparent angles, contact line pinning plays a more important role and consequently drops move faster in the presence of more wetting lubricants. We further demonstrate that the advancing mechanism of drops on LIS involves a combination of sliding and rolling motion. The amount of rolling primarily depends on the drop apparent angle.