Lilac not blooming
Ingham County Michigan
Lilacs do best in full sun (generally, 6+ hours of sun). It may be only a few hours that make the difference. Is the one that is blooming getting more sun than the others? I am not sure what tree coverage/shade is like in your landscape.
The bush that blooms gets the least amount of sun - they all get at least 6+ (presuming the sun is shining)
After a hard prune it can take lilacs a few years to recover and set flower buds again. The one blooming lilac may just be recovering faster than the others due to less stress from the hard prune or other physiological reasons.
This article from the University of Maine can provide more insight into other reasons the lilacs may not be blooming: https://extension.umaine.edu/piscataquis/programs/home-gardening/basicgarden/lilacs/