We describe an on-going 194-671 μm spectroscopic survey of a flux-limited sample of 125 local luminous infrared galaxies (LIRGs) with Herschel SPIRE Fourier Transform Spectrometer (FTS). The survey targets primarily the CO spectral line energy distribution (SLED), from J = 4-3 up to J = 13-12, to probe dense and warm molecular gas that should play an intimate role in star formation and/or active galactic nuclear activities in these galaxies. The program is about 75% finished. At S/N > 5, besides the CO lines, we also detected [N ii] 205 μm and [C i] 370 μm (3P2 − 3P1) lines in every target observed. In about half of the observed targets, we also detected [C i] 609 μm (3P1 – 3P0).