Answer: There is nothing wrong with your lilac plants or the care you are giving them. They send up suckers naturally and prolifically, as you have discovered. You may prune them out or mow them down close to the ground or dig them up and give them to lilac-less friends. I wouldn't dig too deeply into the roots, It will just invite diseases and infections. Lilacs are very tough and don't need a lot of root to transplant succesfully. You are right about systemic herbicides. You would kill the whole plant.
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