One version of the story goes that Lucy's eyes were put out by Diocletian - and in some of those versions this followed her being 'subjected to a common list of legendary tortures -- burning, boiling oil, teeth drawn, breasts sheared, etc.' It's not a Christian thing for her, but a strong female figure thing for her. It's also a gorgeous image. There's also this (it might be where the idea for this tattoo came from since we'd just studied Dante in Rome prior to her getting it) from Wikipedia:
"Dante also mentions Lucia in Inferno Canto II as the messenger "of all cruelty the foe" sent to Beatrice from "The blessed Dame" (Divine Mercy), to rouse Beatrice to send Virgil to Dante's aid. She has instructed Virgil to guide Dante through Hell and Purgatory. Lucia is only referenced indirectly in Virgil's discourse within the narrative and doesn't appear; the reasons for her appearing in this intermediary role are still somewhat unclear to scholars, although doubtless Dante had some allegorical end in mind, perhaps the enlightening Grace that proceeds from Divine Mercy.
In Mark Musa's translation of Dante's Purgatorio, a note is made stating that Lucy was admired by an undesirable suitor for her beautiful eyes. To stay chaste she plucked out her own eyes, a great sacrifice for which God gave her a pair of even more beautiful eyes."