Sandi, is there any way to make it so that the Lilacs can have a mow path around them? That's what I've had to do with some suckering shrubs here that I want to keep. Here, old fashioned Lilacs sucker, but not too aggressively like it sounds like they do in your area. I'm having that problem with an old flowering Quince. I had the bright idea to put a bed around it, and in a couple of years the whole bed was riddled with Quince babies attached to the mother plant. This spring I've been digging out all the flowers in the bed so I can just let it turn back into lawn space and mow the suckers as they show up. Seems the more modern hybrid Lilacs I'm growing aren't suckering as bad.