We investigate theoretically momentum-resolved radio-frequency (rf) spectroscopy of a noninteracting atomic Fermi gas in a spin-orbit coupled lattice. This lattice configuration has been recently created at MIT for 6Li atoms, by coupling the two hyperfine spin states with a pair of Raman laser beams and additional rf coupling. Here, we show that momentum-resolved rf spectroscopy can measure single-particle energies and eigenstates and therefore resolve the band structure of the spin-orbit coupled lattice. In our calculations, we take into account the effects of temperatures and harmonic traps. Our predictions are to be confronted with future experiments on spin-orbit coupled Fermi gases of 40K atoms in a lattice potential.