When I make totes, I topstitch at a 1/4" from the right side around the top edge after the lining is in. It holds the lining secure without riding up. I set a longer stitch because of all the layers, and when I reach a seam, or a handle placement, I lengthen again a bit more just for that distance (or you may find your thread will snap).
You could use a toning thread or a contrast for effect.