  We study the interplay effect of spin-orbit coupling(SOC) and optical lattice
to the single-particle physics and superfluid-insulator transition in ultracold
Fermi gases. We consider the type of SOC that has been realized in cold atoms
experiments via two-photon Raman processes. Our analyses are based on the
knowledge of full single-particle spectrum in lattices, without relying on any
tightbinding approximation.We evaluate existing tight-binding models and point
out their limitations in predicting the correct single-particle physics due to
the missed high-band contributions. Moreover, we show that the Raman field
(creating SOC) can induce band-gap closing in a two-dimensional optical
lattice, leading to the intriguing phenomenon of superfluidity-reentrance for
interacting fermions at integer filling. We present the superfluid-insulator
phase diagram in a wide parameter regime of chemical potentials and Raman
fields. All these results are far beyond any tight-binding model can predict,
and can be directly probed in current cold atoms experiments.
