Lucy _____ Eileen...hm...
Lucy Ann Eileen seems to just be natural, but I wouldn't choose Anne because it is so plain. Let's see...
Lucianna is such a nice name, though, so maybe Lucy Anna Eileen? That sounds very nice...
If you are brace, you could just use a letter. Like, Lucy Q Eileen, Lucy U. Eileen....or maybe not. That doesn't sound so great.
You could pick something to go with Skye (I mean, one girl gets a name like Skye, the other Eileen? One or the other will be jealous.) Like, Lucy Star Eileen, Lucy Cloud Eileen, Lucy Rose Eileen...
How about Lucy Terra Eileen? Terra kind've sounds like Tara, so it'd be a real sounding name, but spelled terra and it's like terra-firma, like, the earth. So, you'd have sky and earth. I like that!