  In a recent experiment by Wu {\textit et al.} (arXiv:1511.08170), a
Raman-assisted two-dimensional spin-orbit coupling has been realized for a
Bose-Einstein condensate in an optical lattice potential. In light of this
exciting progress, we study in detail key properties of the system. As the
Raman lasers inevitably couple atoms to high-lying bands, the behaviors of the
system in both the single- and many-particle sectors are significantly
affected. In particular, the high-band effects enhance the plane-wave phase and
lead to the emergence of "roton" gaps at low Zeeman fields. Furthermore, we
identify high-band-induced topological phase boundaries in both the
single-particle and the quasi-particle spectra. We then derive an effective
two-band model, which captures the high-band physics in the experimentally
relevant regime. Our results not only offer valuable insights into the novel
two-dimensional lattice spin-orbit coupling, but also provide a systematic
formalism to model high-band effects in lattice systems with Raman-assisted
spin-orbit couplings.
