I like it, but prefer
Eulalie.
Eulalia is a little too frilly, while
Eulalie has a bit of a hipper, more accessible feel to it. Plus, Poe!
I think I might be pronouncing it differently than you, because I'm not getting the "you lay" - I'm saying it "Yoo-LAH-lee-ah". Perhaps that's incorrect, but its my instinctual pronunciation.