I’ve worked with a few different lizard and other reptile species, I’ve only noticed them run away and freeze when scared. As most lizards can’t run long distances without a break (as they can’t breathe and run at the same time), there’s not so much point in keeping warmed up for a long sprint, even if shivering did help their muscles stay warm. They’re probably all better off staying still and hoping they get passed over, if shelter is out of running distance.
Monitor lizards can run and breathe, but I never noticed ours shivering at all.
There’s not going to be any point warming up for a long run if you’re a tortoise either…
I did notice pythons ‘vibrating’ on occasion, but it didn’t appear to be a stress/nervous response, as they were just lying out in the open apparently relaxing, and not showing any other signs of stress. Never figured out what that was about, they didn’t do it often.