  We present SPIRE spectroscopy for 9 early-type galaxies (ETGs) representing
the most CO-rich and far-infrared (FIR) bright galaxies of the volume-limited
Atlas3D sample. Our data include detections of mid to high J CO transitions
(J=4-3 to J=13-12) and the [CI] (1-0) and (2-1) emission lines. CO spectral
line energy distributions (SLEDs) for our ETGs indicate low gas excitation,
barring NGC 1266. We use the [CI] emission lines to determine the excitation
temperature of the neutral gas, as well as estimate the mass of molecular
hydrogen. The masses agree well with masses derived from CO, making this
technique very promising for high redshift galaxies. We do not find a trend
between the [NII] 205 flux and the infrared luminosity, but we do find that the
[NII] 205/CO(6-5) line ratio is correlated with the 60/100 $\mu$m Infrared
Astronomical Satellite (IRAS) colors. Thus the [NII] 205/CO(6-5) ratio can be
used to infer a dust temperature, and hence the intensity of the interstellar
radiation field (ISRF). Photodissociation region (PDR) models show that use of
[CI] and CO lines in addition to the typical [CII], [OI], and FIR fluxes drive
the model solutions to higher densities and lower values of G$_0$. In short,
the SPIRE lines indicate that the atomic and molecular gas in the CO-rich ETGs
have similar properties to other galaxies. As might be expected from their low
levels of star formation activity, the ETGs have rather low excitation CO
SLEDs, low temperatures inferred from the [CI] lines, and modestly lower
[CI]/CO ratios.
