Time of day doesn't matter for pruning lilacs or forsythia.
Focus on the season, not the clock. Spring-flowering shrubs set buds the previous summer, so the real rule is: prune them right after they finish blooming, not in fall or winter. The time of day is a non-issue—any cool-ish part of the day is fine, but you’re not going to mess it up by pruning at noon on a Tuesday.
If you prune in late winter or early spring, you’ll cut off this year’s flowers. That’s the mistake people make, not whether it’s 8 AM or 4 PM. So go ahead and prune when the flowers fade, whether it’s morning or afternoon. Just don’t do it in full, scorching heat for your own comfort.
Don’t overthink this. The plant doesn’t care what time you show up.