I like it a lot. And it's totally usable, and shortens pleasantly to Lissy (except one that I used to know who called herself Felix) or not at all.
I taught a Felicity once whose parents had different African home languages. Felicity had two middle names, both meaning Felicity but one in Zulu and the other in Sotho - can't remember what they were now, but it seemed like overkill.