Round-up is not a good idea. May or may not kill the entire lilac, depending on how established the root system is, but it is not a good plan.

Is there a reason why you are concerned about getting rid of the root sprouts? If you seriously want to train the lilacs to be more like a low tree with a visible trunk, then I suppose that would be necessary, but it might not work well. I generally let the sprouts be.

With most lilacs, their growth pattern is 'bush' rather than 'tree'. The tall older stems will not last forever. Many sprouts are started. Some don't last, but the strongest develop, and when the age-weak trunks are going by and need to be cut out, the others are there to replace them.

I have several varieties of lilac, and one really old one is a little more like an low tree, but the other two varieties are not. A single trunk 7-10 years old tends to show severe damage, and doesn't put out much of anything in the way of leaves or flowers. And if the old ones aren't cut out, then the whole bush gets to be unhealthy.

You may have varieties that are like mine. Let the root sprouts be, and cut out the really old wood instead of the sprouts.

Thanks Linda - I usually try to plant some shade flowers toward the front of the lilacs and run into the shoots. But your idea sounds better than that. The bushes are quite old, probably about 10 years, but they still bloom profusely. I try to keep the tops trimmed. They are now about 10 feet high. They were my Mother's favorite flower and mine also, so I don't want to lose them.

Again, thanks for the advice. I'm going to try it this year!!!