If you prune it it will be years before you have any more than sporadic flowers.
If you want to remove it, Lilacs are shallow rooted and easy to remove. Use a heavy rope attached to a trailer hitch.
It looks like some pruned willy nilly or maybe the old main tree like trunks got too big and fellover and were removed.
If you have been to Mackinaw Island they have the largest trunked Lilacs in the world and are supported by ropes and steaks to stop them from falling over and breaking off.
On good thing about an Lilac that does not have all the new growth low down removed is they help support the older large trunks that will eventually keep drooping till they break off or are simply get in the way by sticking out so far.
If you cut it down you will just have bunch of green leaved little branches for years if you just let it grow itself out you will be able to, in three years or so trim it so it is how you prefer or then decide it isn't worth the hassle.
My one neighbor down the street used to have a nice little Lilac bush about five feet high he trimmed every year.
He came down one year and asked me why his Lilac bush never bloomed like mine.
I said stop trimming it.
In a couple of years he got his first few flowers and a decade later it looked real nice with blooms.
Then he moved and the new dude ripped it out.
As a side note, Lilacs burned for firewood give off the most lovely scent.
