Sure we will, just not in the traditional natural-selection sense. In many ways humans have "beaten" evolution by finding medical means to allow "unfit" humans to live full lives, and often pass on their genes.
Evolution in the future could be via technical means, either through advancements in medicine, or with cybernetic implants. If humans could ever become intellectually & ethically pure enough to be trusted with genetic engineering ourselves, that's another form of self-made evolution.
> If we had many lives then each one would be less meaningful.
That's a very personal thing, and just an opinion. With changes in lifespan, attitudes change, purpose changes, and people change their outlook. Once upon a time, humans lived much shorter lives, with many/most not making it out of their 30s. Now life expectancy is in the 70s and 80s. And yet we don't look at this doubling of our lifespans and believe that all that extra time robs our lives of meaning. So why should that be the case if we could live to be 500?
> We’d at least need to put age limits on political participation.
Perhaps, but that should be a floating limit that gets adjusted upward with life expectancy. If people regularly lived to be 200, maybe 190-year-olds wouldn't be fit to serve, but a 100-year-old? Why not? And if we managed to push that to 400, those 190-year-olds would start to seem pretty relevant; it would be an injustice to deny them participation in the political system.
Regardless, our idea of society itself would need a huge overhaul even if our lifespans were doubled, let alone made effectively limitless. Political participation would likely be the least of our worries.
Citation needed; because that's commonly believed to be average life expectancy - brought down by infant mortality. If you made it past ~5 years old, you had a good chance of living to 60-80.
"The days of our years are threescore years and ten" - Psalm 90:10, the King James Bible.
"A man will spend ten years as a child before he understands death and life. He spends another ten years acquiring the instruction by which he will be able to live. He spends another ten years earning and gaining possessions by which to live. He spends another ten years up to old age, when his heart becomes is counsellor. There remain sixty years of the whole life, which Thoth has assigned to be the man of god." - A passage from The Insinger Papyrus, in the Ptolemaic period"
Not as a species though. We just have to keep reproducing more of us that are good at staying alive and also reproducing to evolve. You and I theoretically could live forever in the same state, and still, our species would evolve via our offspring and theirs and so on.
If you're actually worried about evolution you'll want to bring back eugenics. Current selective pressures are quite relaxed, leading to an increase in deleterious mutations and rising future healthcare costs.