To answer the question:
Live Paint allows editing the shape borders and the paint follows as long as the paint is not expanded. After expanding you must edit the shapes separately.
In the left there's a non-expanded Live Paint result
In the middle a couple of new anchors are inserted to a borderline and the anchors are dragged a little off with the direct selection tool
In the right the anchors are made smooth with the anchor point conversion tool.
BTW Check from the Illustrator documentation (by Adobe) how to draw and edit curved paths. I guess most of us would draw curved paths from the start for this purpose.