One detail: "supple" can be applied to material, particularly leather. Leather that is very soft and flexible is "supple," but is not "lithe."

To me, no. And I'm not going to run to the dictionary for its permission! I would tend to use lithe to describe positively the physical performance of a person doing something where the wide range of his joints was intrinsic in the performance. Whoah! Whereas supple steers me more towards the range of motion of his joints. So, Sri Lankan people have very supple fingers. I wouldn't say they have lithe fingers. Lithe more describes the whole body. But, I think you could use supple to describe the whole body too. I wouldn't spend too much time differentiating the two. But, as I indicated, you don't hear people talk about lithe wrists. It's very common for a lot of synonyms to be not quite synonymous, especially when describing different things. Hope this helps.

I think you're spot on. To me, lithe implies slim and elegant. Supple implies agile, flexible and/or soft (to the touch).

I don't think the difference is about beauty, but rather a whole person is lithe or supple, whereas muscles are only supple (not lithe). I haven't thought about it in great detail but this feels right.