My daughter is called Nicole Jean and my son Andreas. I do love the name suggested by your daughter; Lillyanna.
Also I like the french names Jeanette and Yvonne. My neighbour just had a daughter named Marielle. I also like many old-fashioned names: Sophie (in Norway: Sofie) and Tuva.
My nieces(grown up now) are called Maiken Aurora (from the northern light; Aurora Borrealis (Lat.))and Kristina. Nephews and their sons are: Anders, Markus, Jonas, Lukas, Mads and Marius.
I love the Irish names too of both girls and boys. And There is a Turkish boys name I love; Emre. Another boys name I love is Darius; don't know why but it rolls so nicely, somehow.
Good luck to find the perfect one
Hugs
Anne