The concept of "life renewal" appears to have changed over the course of the production process.
The early draft of the film script (as mentioned above) states that renewal means reaching the top of Carrousel and touching the rainbow/crystal, following which the lucky person is allowed to live beyond 30 (presumably another 30-year cycle) IN THEIR CURRENT BODY. Note the conversation in the draft script between Francis and his female Lastday friend (who says that she can join them in their late-night activity provided she reaches the top of Carrousel). However, this female character and her statements are removed from the final film.
Now let's look at what is shown onscreen in the final film. Firstly, we should note the DVD commentary by director Michael Anderson, who says that for a person to be renewed, he/she must touch the white crystal at the top of Carrousel. So there is no question about what the Lastday people have to do. But what happens to them when they do touch the crystal? Though not explicitly stated, it is possible to arrive at a reasonable answer after considering the following onscreen references to the ritual made by several characters:
1) At the start of the film, Francis tells Logan that "there'll be a couple of Sandmen in [Nursery] tomorrow", as "some of our guys are on Carrousel tonight, and Sandmen always renew."
2) When Logan is told by the Computer that there are so many unaccounted missing Runners, he says "maybe most of them renewed on Carrousel."
Now, 1) and 2) clearly imply that those select few who are "renewed" also undergo vaporization like everyone else, LOSING THEIR CURRENT BODY but because they touched the white crystal, they've earned the privilege of having their disembodied souls reincarnated into newborn babies in Nursery. Hence the Computer's famous statement "Be strong, and you will be renewed". So no one's original physical body ever lives past their 30th birthday.
Hope this helps.