If you thought it was over used 5 years ago, then I don't get why you think its not going to be regarded as over used still now. The trouble is, that there will lots of older Lilys running around who aren't just going to disappear. Your Lily might not have quite so many in her class but as soon as she leaves school, that isn't going to be as relevant. She'll be just another Lily just a bit younger.
'Over use' tend to last for a generation. Think Claire, Sarah, Emma or Deborah, Tracey, Sharon or Margaret, Patricia, Christine, Barbara. All of which 'place' when you are born to within a few years.
If you want something that isn't over used you have to look away from the most popular names of that particular generation and find something that fits with the time but hasn't peaked or is about to peak quite so spectacularly. The 'safe' ground is generally regarded as something that's 'mid table' in around the 50 - 300th ranked mark. Not too out there but still pretty usually without being mega popular.
My point being that if over use bothers you, then going for something that was top ten so recently, probably isn't the way to go. However if you really like the name then it shouldn't matter how popular it is.