I had some that budded, half bloomed, the cold snap arrived and they never finished blooming. It affected about 5 different varieties in my yard.

Some sources say to chop the whole thing back to about 6 or 8 inches high. I would do that now, if I chose to go the more drastic haircut route, because to do so in the wintertime or even fall could run the risk of new shoots getting freezer burnt. Especially as you are in Z5. The other method for really old thick lilacs is to chop off one-third (or in your case, one or two) of the really thick old growth this year, then another one next year and so forth. This preseves more option of continuous bloom, if any. Personally I would use the former method. Also, lilacs like sweet soil, so a bit of lime or wood ash might be in order if your soil is acidy.

the term is rejuvenation pruning ... here is a link of vids ...: https://duckduckgo.com/?q=rejuvenation+pruning+lilac&t=ffcm&iax=videos&ia=videos interior wood does not heal like a broken arm might... as such.. staking it up is useless ... if that is your neighbors house.. why are you messing with it??? ... just helping ... ???? it is a full sun plant.. the fact that it is leaning away from the house.. means its stretching for the sun ... and that is the base cause of what the cause was ... i also suspect ... that trees planted decades ago.. when this monster was planted.. have now decreased light .. is it in shade part of the day.. other than from the house ... prune after blooming.. use the flowers on the ground for indoor cut flowers .. but wait ... if you want straight flowers.. if you can rig it upright somewhat ... it might help flower development.. for the short term ... otherwise.. after bloom ... start the rejuvenation process.. which is usually a 2 or 3 year process ... but you can also do it all at once ... imo ... with no insult to the root mass.. you might be amazed how fast it regrows this season ... ken

Lucky! That's a beaut! IMO, it is too large and takes up too much ground space to remain in the shrub form, and needs to be turned into a multi-trunk tree form. Decide on what degree of spread, in a conical shape you'd want its trunks to form. It could be narrow or wide, but I'd suggest something in the middle will work best ... around 45* - 50*. Preserve all trunks that fall within that cone shape and completely remove any trunks that fall outside of it. (Hopefully, between the two sketches and the description, you will get the idea.) For the tree form, there generally isn't any reason to reduce the overall height of the plant and you can allow it to grow as tall as its nature allows. (If you have your own reason, that we don't know anything about, you can do it, but it will be a fair amount more work each time you do it.) While you probably won't reduce overall height, you will want to shape the canopy round, as in a dome shape. This means there will be a portion of the canopy that gets no cutting at all, and some of it which is "lightly" snipped so as to create the dome shape. In the illustration, you can see that from the view shown, a little of the canopy outer width needs to be removed. You would do this all around, as needed, as you appraise the tree canopy shape from each side. If a portion of the canopy's branches are not long enough to reach the envisioned dome shape, you won't cut any off of them. You'll need to let them grow in order to catch up with the others. Over time, it will even out until the dome shape becomes near perfect. In order to expose the trunks, you'll envision a horizontal line at 50% of the tree's total height. Remove every branch, twig and foliage below this line, while leaving every trunk (that falls within the predetermined cone.) At the beginning of cutting it might seem like a mess of wood seemingly going every which way. If a piece of wood is more vertical than 45*, it's a trunk. If it's more horizontal than 45*, it's a branch. Don't try to make one be the other. Updating this lilac from a shrub to a tree is not something you would pussyfoot around doing over time. You'd do it start to finish in a couple of hours, or whatever part of a day it take you ... AFTER blooming is finished, of course! (Annual updating would happen at the same time of year.) There is a tremendous lot of branching and foliage to be removed below the bottom-of-canopy line. The result of removing so much foliage is that within a few short weeks, the tree will be putting out a tremendous amount of new growth, trying to replace what it lost. Most of it will be replaced in an upward direction, but there will be some to come below the canopy line or outside of the dome shape. As the rate of new growth begins to slow, do a touch up following all the same rules, except, don't raise the bottom of the canopy higher (to 50% of the new, possibly higher total height.) You'll do that next year. Each year it will become more perfect. You can accomplish all this work easily with a Corona or Fiskars 10" folding pruning saw, a STURDY pair of loppers and a hand pruner. Be sure to post a photo of the finished work. (And do a good job so that shame is not cast on me.) :-)