It takes a bit of explaining, Sarah 15:34 Mar 18, 2015
«Светиться», as used here, comes form «засветиться», the verb in the perfective form, meaning “to be exposed” (as applied to photo or movie film). Once exposed to light, the film cannot be used again.
Figuratively, «засветиться» means to show up, to be seen, be noticed, with the implication here (in the context of the novel) that once seen, the woman’s secret game will be up in smoke.
That gives «лишний раз» a new edge: not “an EXTRA time” or “once AGAIN and unnecessarily” as usual (and as suggested below), but at all, meaning “once too often”. One time, in the context of the novel, IS extra. The more so that Maj Kamenskaya had never been to Samara’s convict colony before, as you already know. ;-) | 
peer agreement (net): +2