Lollipop.
Joking, joking...
Lolly is adorable and you could use it as a nickname for any name containing an L. Honestly. I was thinking,
Lola sounds right, and then I remembered that
Lola is a nickname for
Dolores. If you can get Lolly out of
Dolores, well, anything goes, I say. Names with a "LAH" sound would be even better, like
Lara ("LAH-ruh," not "LER-uh") and
Alana ("uh-LAWN-uh").