i love emmet, i rarely hear that name around, as for lily i had 5 lilly's in my pre-school class last year. but they all had variations and we're called lily for short. for example lilliana, lillian, lilly, lily, lilith. i don't have any lily's this year but there are a few in the centre.
it's still a lovely name though and there are other similar names such as lylah, lilah, lyla.