which champion (or champions) can be played in a variety of lanes and roles?

Most versatile champ in the game, can play her as a top, jungle, mid, or support without being called out for trolling. Used to be able to play her as a marksman, but she's weak enough at that it's questionable (in rift - she's a solid marksman in Dominion and Treelines where range gets crapped on).
Her build is litterally the same thing in any lane as any position as well, which makes things easy. You get to be APC/ADC/Support with the same AS/AP build.
Other than that - if you're looking at flexibility and a kit that can adapt, any champion with 7 abilities rather than 4 is going to offer a solid 3 lanes they can pull off.

You actually need to build differently depending on the lane more often than not here though. They have flexibility in their direction, but they don't get to maintain doing everything well into overtime like Kayle. You need to itemize for it. Lee Sin will be an assassin, fighter, or tank based on his itemization for instance - he won't be all 3 at once after a certain point.
I'd also strongly recommend staying away from champions nobody's exactly sure on where to put them.
Some people usually recommend champions like
in such topics because those champions are seen in a wide range of lanes.
But those champions are seen in a wide range of lanes more because they're terrible and everyone's trying to figure out what lane they should go in rather than those champions actually being really flexible and good to the point they can go anywhere, which makes them the exact opposite of what you're looking for.
TLDR:
