In Illustrator how to maintain an assigned graphic style after using Live Paint Bucket

In Illustrator, I noticed that any graphic styles assigned to various paths are removed when the Live Paint Bucket is applied. For example, I initially have the following:

Notice I have the "Green stroke" graphic style applied. When you select the path, the "Green stroke" highlights in the Graphic Styles panel. I then go on to use the Live Paint Bucket:

When I then select the same path, the "Green stroke" graphic style is not applied. Yes, the appearance does not change, but the path is no longer associated with the specific graphic style. (In addition, if I then reapply the "Green stroke" graphic style, it applies it to all paths making up the Live Paint group including the red rectangle.)

If I then try expanding the Live Paint group, same result. The graphic style is not associated:

Is there a way to maintain the graphic style assignments or apply different ones to individual paths after Live Paint Bucket is used?