To be honest, I'd bet on the lumbar arthritis playing a role here...or other spine related nerve compression. Especially since it's bilateral. You don't have to have any back pain (and many don't) with nerve related pain of this nature.

Do you still have this pain even if you lift one leg (just enough to take the weight bearing off)? I don't mean lift it off the floor, just take the weight off.

Since it only occurs while standing still, there must be some sort of compression in this position. You should contact your neuro, or orthopedist that specializes in spine.

I assume that the pain goes away when walking?