I suppose it depends on which side of the pond you are on. In the UK, it's my understanding that
Lilian is the default spelling while in the US, the name is usually spelled
Lillian so I can see where
Lilly comes from.
Personally, I prefer
Lily. After all, the flower only has one l. I just find the other way strange looking. In addition, other countries have variants of the name and they only use one l (
Liliane,
Liliana). Also,
Lily after the flower looks less like a nn than
Lilly which just looks short for
Lillian.