This study uses r-band images from the Eighth Data Release of the Sloan Digital Sky Survey (SDSS DR8) to study bars in lenticular (S0) galaxies in one of the nearest rich cluster environments, the Coma cluster. We develop techniques for bar detection and assess their success when applied to SDSS image data. To detect and characterize bars, we perform 2D bulge+disc+bar light decompositions of galaxy images with galfit. Using a sample of artificial galaxy images, we determine the faintest magnitude at which bars can be successfully measured at the depth and resolution of SDSS. We perform detailed decompositions of 83 S0 galaxies in Coma, 64 from a central sample, and 19 from a cluster outskirt sample. For the central sample, the S0 bar fraction is 72^+5^-6%. This value is significantly higher than that obtained using an ellipse-fitting method for bar detection, 48^+6^-6%. At a fixed luminosity, barred S0s are redder in g-r colour than unbarred S0s by 0.02mag. The frequency and strength of bars increase towards fainter luminosities. Neither central metallicity nor stellar age distributions differ significantly between barred and unbarred S0s. There is an increase in the bar fraction towards the cluster core, but this is at a low significance level. Bars have at most a weak correlation with cluster-centric radius.

Cone search capability for table J/MNRAS/439/1749/tablea (SDSS data and morphological classifications (table A1), and bulge+disc+bar decomposition parameters (table A2) for the 83 S0s in this investigation)