We analyze Galaxy Evolution Explorer UV data for a system of four gravitationally bound groups at z = 0.37, SG1120, which is destined to merge into a Coma-mass cluster by z = 0, to study how galaxy properties may change during cluster assembly. Of the 38 visually classified S0 galaxies, with masses ranging from log (M *)[M ☉] ≈ 10-11, we detect only one in the near-UV (NUV) channel, a strongly star-forming S0 that is the brightest UV source with a measured redshift placing it in SG1120. Stacking the undetected S0 galaxies (which generally lie on or near the optical red sequence of SG1120) still results in no NUV/far-UV (FUV) detection (<2σ). Using our limit in the NUV band, we conclude that for a rapidly truncating star formation rate, star formation ceased at least ~0.1-0.7 Gyr ago, depending on the strength of the starburst prior to truncation. With an exponentially declining star formation history over a range of timescales, we rule out recent star formation over a wide range of ages. We conclude that if S0 formation involves significant star formation, it occurred well before the groups were in this current pre-assembly phase. As such, it seems that S0 formation is even more likely to be predominantly occurring outside of the cluster environment.