I was undecided about whether to just line the bottom, or to line the flap, too. I wanted the stability, but it involved making a button hole to line up with the wacky knitted buttonhole. In the end, I obviously decided to tackle the buttonhole. I used the fancy auto-buttonhole feature on my sewing machine. It worked pretty slickly. The sewing of the lining isn't my best work, but it'll do.
Ps. I still couldn't be more thrilled with my table and chairs. I only wish the weather had been a little nicer today that I could have enjoyed it more. Although, truth be told, I enjoy just looking at it through the window more than one might expect.