Using Live Paint Selection Tool, we can choose sections of the Live Paint objects, areas and segments of contours, assigning fills and color to them.

But what we can assign is rather basic (the same as for live characters, and the related request about the same deal is here: http://illustrator.uservoice.com/forums/333657/suggestions/46545787)
We can’t assign a brush, change order of appearance attributes, add a second fill and offset it, assign any effect to it, distort or roughen — only fill under stroke, no stroke alignment (even though the panel lies it can be done), no arrowheads... at least dash count as basic apperance.

We need more control over it. We need to be able to control appearance for Lve Paint selections fully.