I think it is the vast rise in names that cause them to date. Names that are popular over a long time tend not to date be as faddy as those which have a sudden rise.
So has Lily had a sudden rise...?
If you have a look at the name stats between 1996 and 2010
Lilly rose from 375 (89 births) to 39 (1512 births)
Lily rose from 85th (651) to 4th (4257)
So it has gone from 740 babies in 1996 to 5769 babies in a 14 year period.
And that's before you add in the hyphenated names...
Lily mae - from 3795 to 241
Lily rose from 3795 to 268
lily may from 1914 to 285
lily mai from 0 to 480
lily ann from 1755 to 730
lily grace from 0 to 758
and there's similar rises for these hyphenated names but spelt Lilly and there are the other spelling variations to consider such as Lillie.
Whereas, if you compare it to a name not considered as Faddy - say Elizabeth (often cited on here as a true classic and therefore not easy to date) over the same ten year period, it went from 26th to 49th in the same 14 year period.
Similarly, Sharon was not invented or a new name (apparently been around since the 1920s) but it reached no 10 in the UK name stats in the 1960s and was 17th in 1974, but has not been in the top 100 since the 1980s (according to wikipedia) - its the huge rise and decline in popularity that makes it 'faddy'.
So yes, I would consider Lily to be faddy.