Is it wise to prune off the spent dead buds to enhance growth for next year?

I learned to cut every year one third of the bush. Yes, that would be essentially this year's blooms or what is left of it.

But it's getting late to prune lilacs. They start setting new flowers soon after the previous ones fade, so they should be pruned right after they finish blooming.
https://www.arborcare.com/blog...

The new bloom is right behind the old bloom, you have to make sure you do not cut off the new bloom.
Cutting them off technically improves the bloom for the next year.

https://www.swansonsnursery.co...

I will assume that by deadheading you mean to cut the dead part off. This is not pruning like Ursula and NMoasis alludes to.

Next season's flower buds have already been produced, and they are easily seen, even now, as fat buds, usually in pairs at the ends of the twigs. Far more often, these are not immediately below the dead flower, but they could be. Nevertheless, the fat buds will be evident if they are there.

Pruning dead flowers at this time of year will have no consequence to the future growth. But theoretically, pruning the spent flowers in early to mid summer, while they are still green would. At that time, the lilac is pumping in energy and nutrients to make seeds, and removing them would redirect that energy to the rest of the plant. Because the flower panicles are long dead by now, cutting them does not redirecting anything. However, you can still cut them off if you think it improves the look.

I fixed a typo, cut off the dead bloom but be careful not to cut off the new bloom.