There has been uncertainity about the relationship between Lily and Dave. Diana's dad is also named Palmer meaning the only logical option for all three having the same surname is that Dave Palmer is Diana's fathers blood brother.
After the death of Diana's father and Lily's husband. Dave has stepped up to look after them. Dave has never married. He brings a great balance to Lily and her disdain to the Phantom.
Lily has a dislike for the Phantom. This could be because of her grief for her husband leaving her and she is worried about the Phantom doing the same for her daughter.