Lily is the name of the flower.

Lilly or Lillie is traditionally a woman's name, short for Lillian.

Of course there are some women named Lily also. You can name a kid anything you damn please, and make up any spelling you like. (At least in the US. I believe there are some restrictions in France?)

Lilly is also a surname (as in Eli Lilly).

Pointing out spelling problems like this is usually helpful, because search engines like Google won't find "lily" if you search for "lilly", and vice versa, and a lot of people don't know they should try more than one spelling.

A lot of information on the web is posted by people who can't spell, therefore it's often a good idea, when searching, to try a "wrong" spelling even if you know the "right" one.