Does a photograph lie? Does the caption?
It is more complicated than that. A photograph, an unmanipulated photograph let us stipulate, represents a literal point of view. As far as that goes, it is "true":
https://en.wikipedia.org/wiki/Truth_claim_(photography)
A caption has more scope for lying, it can be simply factually wrong, it can be willfully wrong, such is the nature of language. There is no equivalent of the Truth Claim for words.
But to get at the thing you need to have some notion of what you even mean by truth. Not to scramble down a philosophical rathole here, but, in my favorite example, "what was the cause of the First World War" jumps to mind. There is no glib singular "truth" here, and there may not even be a lengthy book-sized truth to be had here. The one thing we can be sure of is that the assassination of Ferdinand was
not in any meaningful way the cause.
Once you have your arms around something like the "truth" of a situation, assuming that yours is one of those where it is possible to get your arms around it, what then does it mean to for a photograph, or a caption, or a combination of them, to be true?
Must it align factually with the little details of the truth, even if the overall impression it yields is the opposite of the big picture?
Or may it skim over and play games with the little details, if the overall impression aligns with the "truth"?
Must it do both? Must it, that is, align at every possible level of detail?
These are complicated questions, once you start digging. A reasonable, albeit flawed, starting point is
Believing Is Seeing: Observations on the Mysteries of Photography by Errol Morris. I find his analysis flawed, but the raw material he digs up is mostly excellent, except the bits about the clock on the mantelpiece as shot by Walker Evans.