If lifespans increases then the population will still grow for some time. And it's increased steadily for the past 70 years.
Having said that, I suspect that once we crack aging, we may blow past the current limit and see a relativly sudden jump in lifespan
https://www.reuters.com/world/india/india-reports-daily-rise...
https://api.nationalgeographic.com/distribution/public/amp/s...
For every increment in lifespan, population grows until death rate matches whatever birth rate has been achieved.