It looks like it's in too much shade for it to do as well as you would hope - that could explain the lower, bare branches.

There are a couple of ways to approach renovating the shrub. You can cut back a third to one half of the oldest stems to the ground as soon as the bloom period is over (check when that is in your neighborhood if no flowers on this shrub). Next year at the same time, you do the same with next 1/3 - 1/2 of the old stems (and again in the third year, if you are doing this by thirds). By the end of this process you will have a drastically scaled back shrub with a lot of new vigorous growth coming from the root crown.

Alternately, wait until mid to late fall and cut the entire plant back to about 6-10" from the ground. Next spring remove all the new shoots except several of the strongest to develop into the new framework of the shrub. It will take awhile before the shrub regains any sort of 'normal' appearance and at least 3 years before it blooms again.

Either approach will be temporary at best. The shrub will regrow to its former size eventually. If my assumption is correct that this lilac is not receiving enough sun, then the new growth will be long and lanky and you will soon have the same result as you do now. Lilacs do best in all day (8 hrs.) sun.