Lily sounds like Lully in Glasgow!
... and in NZ! 
Most names are cyclical, but some are much more so than others. I know what the OP means about David - people of my generation know at least three Daves, whereas no one is calling their baby David
now.
Same with Michael, Mark, Simon, Peter, Charles - all classic, solid names that are out of favour now - instead George, James, William, Daniel - and the ubiquitous diminutives are much more in favour - Harry, Charlie, Alfie, Archie, Freddie, etc.
Girls names that you can't move for are all listed above.
It's funny, because there are so many names out there - lovely, classic, elegant, perennial names that are under-used and won't date, but people go for the same old Ellies, Millies, Evies, Evas, Amelias, Chloes, Graces, Sophias, Olivias, Ellas, Islas, etc...