  We present [CII] observations of 20 strongly lensed dusty star forming
galaxies at 2.1 < z < 5.7 using APEX and Herschel. The sources were selected on
their 1.4 mm flux (S_1.4mm > 20 mJy) from the South Pole Telescope survey, with
far-infrared (FIR) luminosities determined from extensive photometric data. The
[CII] line is robustly detected in 17 sources, all but one being spectrally
resolved. Eleven out of 20 sources observed in [CII] also have low-J CO
detections from ATCA. A comparison with mid- and high-J CO lines from ALMA
reveals consistent [CII] and CO velocity profiles, suggesting that there is
little differential lensing between these species. The [CII], low-J CO and FIR
data allow us to constrain the properties of the interstellar medium. We find
[CII] to CO(1-0) luminosity ratios in the SPT sample of 5200 +- 1800, with
significantly less scatter than in other samples. This line ratio can be best
described by a medium of [CII] and CO emitting gas with a higher [CII] than CO
excitation temperature, high CO optical depth tau_CO >> 1, and low to moderate
[CII] optical depth tau_CII ~< 1. The geometric structure of photodissociation
regions allows for such conditions.
