[sfpotter]

The concept of a Lipschitz function comes from mathematical analysis; neither computer graphics nor numerical analysis. It's straightforward to find the definition of a Lipschitz function online, and it is not in terms of its derivative. If a function is differentiable, then your quote applies; but again, it isn't the definition of a Lipschitz function.

I'd say this is a little pedantic, save for the fact that your function of interest (an SDF) isn't a differentiable function! It has big, crucially important subset of points (the caustic sets) where it fails to be differentiable.