Simply dig up the sucker with sufficient roots after leaf fall and transplant them to another site. Sucker should be at least 12" long and as thick as a pencil - with as much of the root attached as possible.

Leave a few of the lilac suckers intact so the lilac has branches of varying ages.

I have @125' of common lilacs planted in 1900 that seem to top out at 15' or so in height - judging from the old trunks, I'd say they were originally planted 3' apart. Someone's going to argue this is too close, but 109 years of beautiful growth and spectacular blooming seems to tell me someone got it right. What suckering I do get, I leave so Ive got really dense screening ground to crown.

Spring came somewhat grudgingly, but everything catches up quickly - it's going to be a massive lilac bloom year.

Not sure about killing off raspberries - cut them down and dig up the rootstock? Or paint the newly cut down stems with Roundup rather than spraying? Roundup should work only on the cut down raspberry plants and not transfer into the soil.

The lilac suckers could always to potted up, watered, and kept in semi shade until they're ready to transplant.

raspberries are a real pain to get rid of If I really wanted them gone I would hit them hard with round up all summer evenually the roots should give up

Your yard must smell incredible