What sort of lilac was it? Even the first picture doesn't look like any lilac I know of. Did it flower? The other leaves are definitely not lilac. If you look you'll see they are arranged alternately, not opposite.

The alternate leafed plant looks to me like buckthorn, most likely glossy buckthorn/Frangula alnus, a nonnative invasive that gets spread when birds or other critters eat the fruit and then deposit the seeds elsewhere. You want to remove it. I would cut out what you can (if you can't pull it out) and then check once a week and remove every leaf you see until it is gone. Since it is growing up through the middle of the lilac, I don't think you can use brushkiller, even if painted or dripped on it, without endangering the lilac.

i would cut the unwanted plant at ground level.. and BRUSH a stump killer on the fresh cut .... do it all the time... never killed the favored plant ...

and if you want to kill the lilac.. do the same ..

keep in mind.. with no insult to the L root mass ... it has HUGE potential.. to grow right back into that huge plant it was prior ... without severe annual pruning ...

google REJUVENATION PRUNING OF LILACS .. for the suggested method or pruning.... OTHERWISE KNOW.. IN MY WORLD.. WARPED AS IT IS.. AS.. BEATING IT BACK WITH A STICK.. LOL ...

ken

The 1st photo (w/opposite leaves) is Lilac. The other photos with alternate leaves is a cherry of some sort (bird sown most likely).

Do you know what sort of lilac is it Smivies? It's not Syringa vulgaris for sure. But there are plenty I'm not familiar with.

Compare with Syringa pubescens subsp. patula 'Miss Kim'

Thanks, Smivies. Can't say I've ever knowingly seen one. S vulgaris is seen in older gardens but other than that they're not particularly popular here.

Thanks everyone for the advice. I cut out the invasive plant. My next question is how should i prune it?As you can see by the pictures what I did last year didn't work. There is growth (not pretty) on it but all the tiny branches are really delicate and you can't really
touch them without them breaking off. Is hope gone for this lilac?

Right now, do nothing. It's already been severely pruned and starting to regrow. Doing it again so soon has a very good chance of killing it.

Wait until the fall of 2018 (or after flowering spring 2019) at least to do selective pruning for improved branch structure.

in the meantime.. i suggested you google up rejuvenation pruning ... ken