If we were to develop a dancer champion it would assumedly be because we felt such a champion would allow us to:
- Offer new gameplay of various forms (new skills to master playing as said champion, the ability to do new things in the game others can't and an impact on how teams think about strategic play).
- Tell a story and present a personality we hadn't already included in the game
- Offer a distinct visual appearance, silhouette especially
- Do all of the above better than other concepts we were considering at the same time (e.g. if looking for a new assassin we'd want to be confident that the dancer idea in question was better than other assassin ideas on the table). Dancer is an idea we've talked about occasionally, so far though we haven't hit on a version we felt was stronger than other options we've been looking at.
To dig into part 1 above, since gameplay's what you've mentioned in your post:
Dancer as an archetype's generally about physical control - agility, discipline, movement, grace and/or power, etc.
Assassin or light fighter are the roles I'd consider most likely to be a good fit as a result, since those attributes align well with the expected actions and fantasies of those roles.
Could potentially make an argument for support as well, Sona's existence as an 'inspires allies with music' champion occupies a lot of the space there though.
Could also go with something a bit unexpected and go for a mage instead (ritual based caster, with long cast times, with dance acting as a channel for magical power)
Regardless of which choice of role you opted for I'd be inclined to start by looking at some form of combo caster (whether melee or ranged), with ability chaining representing dance flow, and different effects based off whether abilities were used as a setup or finisher. Very easy to get into over complicated design with that sort of approach though, so would want to either have some fallback options or be willing to kill the concept if it wasn't showing promise.