The dispute is over the photo ops that take place after the swearing in ceremony.
Now, do they lie? Sure, after all they are Congress-critters.
My only question would be why this particular Congress-critter wants to have a photo taken showing me that, Fur Shur, he intends to lie to me.
That's rather stupid doncha' think.
Yes, but he is betting that the vast majority of people won't know that the Koran encourages lying to infidels.