I'm very confused by this. The entire point and exercise of language is to define and categorize things around us. This applies for words like "god" as much as words like "pencil" and "running" and "bystander." All language is a human construct... it's all "made up" by us.
At any rate, the first and most obvious question to ask is to look at what it is you're labeling a god and ask if it is reasonably capable of lying. None of the gods I worship on any regular basis are capable of lying, because they don't possess the attributes necessary for deception. I imagine humans might project lying onto them, but that's the human's attribution. Sometimes I will say Blue Jay is a liar, because it's feathers are not actually blue, but black; yet Blue Jay itself is not really a liar, that's an attribute I am applying to it based on my human point of view. There are some plant spirits I could call liars too, because they engage in mimicry to manipulate animals but again, me calling that "lying" is something of an anthropomorphism and attribution.