  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 characterise bars we perform 2D bulge+disk+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 outskirts 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 0.02 mag. 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.
