These two goals aren't mutually exclusive. More learning and persisting knowledge works great with long lifespans. Evolution acts faster when children are born quickly. You can have a new generation every 20 years and still have lifespans approaching a century.
The optimal solution IMHO is to maximise lifespan, and encourage teen pregnancy. Great grandparents, when they're starting to slow down at either work or academia, take on raising their great grandchildren, so their grandchildren can get their PHD and do their big research project.
Natural selection favours those who can most efficiently create children who go on to create more children. Nowhere in there does it require those to die. They can try again to produce favourable offspring, they can teach their descendants things, or they can go do literally any other thing - they've already put the wheels of evolution in motion.
But if they were mutually exclusive
You need a human to:
- Develop and learn basic fundamentals (walk, read, write, count, minimum science, etc).
- Learn all knowledge in a speciality.
- Perform research within that field.
- Go through rounds of peer review improving their research.
- And then repeat.
School and early learning could be tightened a lot, but we need to learn to socialise to, reproduce, research, and teach, so I wouldn't want to tighten this below 16 years.
Reproducing, I define as getting offspring ready to survive on their own, which is another 16 years, but that can be done in parallel to the other things part time, and could be shared responsibility with others (teachers, partner(s), babysitters), so I'm adding only 4 years for that.
Learning all you can about a speciality I'd class as getting a PHD - so 7 years.
Doing a research project, getting it reviewed, and released, could be anywhere for 6 months to 10 years. Lets call it 10 years. You may get 1 big project done, you may get 20 little ones done. I'm also guessing a bit high because your first work is rarely your best, and once you're acquainted with a subject it makes sense to spend some time as the expert (rather than do one project, and then let the speciality stagnate for another 20 years until another expert comes).
Sum them all up and that's 16 + 4 + 7 +10. 37 years.
I reckon that's a ballpark answer. It improves the pool of human knowledge slightly with each generation, which is a little above the goal of your question, but this will make up for occasional losses of knowledge if things go wrong when the threshold is quite tight.