Going back to philosophy 101 the concept of truth and lies only applies to propositions; formal statements about the nature of things. A proposition that on investigation turns out not to be the case is untrue, a lie in other words. So the question devolves into: What formal statement does photography offer about its relationship to subject matter? Interestingly, those who insist that the camera lies or photography lies never offer (never think?) that there is a proposition to state and then to test.
Here are a couple of illustrative examples of silly propositions:
"A photograph of a tree is not a tree therefore photography lies". I can't remember a case of anyone credibly insisting the photograph should be physically congruent with its subject.
"A photograph is cropped from reality therefore photography lies". Does anyone sensibly require the photograph to be as big and inclusive as the universe in order to be true?
On the other hand: "All points in a photograph bear a one to one relationship to points in the subject matter". This is likely to be necessarily true of photography because of the physical causality of the process.
There are several other propositions that are also true of photography and it is a pleasant diversion to think of them.