Personally, I think
Lily is too much of a stretch from
Caitlin. If I knew a
Caitlin called
Lily I would assume the nickname came from somewhere aside from her name (like her middle name, or she was very fond of
Lily's as a child or something...)
If I met
Lily and
Rose as siblings I would think their parents were garden-mad. Individually, I think
Lily is very cute and pretty, and
Rose is sweet, but for some reason (and I really don't know why, given how popular
Lily is at the moment!) it doesn't sound as 'fresh' to me as
Lily does.