Do you trim off this year dead flower or do they stay?
My lilac tree is about 15' tall and I am in the process of pruning it to about 6' tall.
You should "deadhead", prune off the spent flowers.
Nine foot height reduction of a 15 foot plant is very extreme and can be detrimental. The Best Management Practices standard for the tree and landscape industry is to not remove more than 25% of the foliage in a one year period. More than that is stressful for the plant physiology, and it destroys the natural form and beauty. And it will cause rampant regrowth that will require extra maintenance.