what a joy that you posted this! i have decided to plant some lilacs this year and am just setting off to learn about them. so thank you!

You won’t kill it by rejuvenating it, but the usual wisdom is to do that over three years — cutting out one-third of the oldest (thickest) stems each year to gradually allow new (thinner, shorter) wood to repopulate the area. One other issue is whether it’s growing “on its own roots” or grafted onto a sturdier lilac rootstock. Cutting the whole thing to the ground all at once can also sometimes allow the rootstock to overcome the desired parts of the plant.

As for that tree…oh, dear. Needs to go at once (well, not if it’s snowing, but you know what I mean). It may keep resprouting, too, so see if you can dig it out as well, or be prepared to cut it down to the base again and again till you kill it.