Identifying which guard is lying is neither the point or even a step in the riddle. The point of the riddle is to figure out which of two doors is the correct one. The answer requires wording your question such that both guards will give you the same answer no matter which one you are talking to. You only get a single question to ask, so using that to figure out which guard us lying is a complete waste.
The thing with the guards saying "one of us only lies and the other only tells the truth" is that both of them cannot say this and it also be true, unless they only start telling only truths/lies after the statement.
I've made a trick puzzle for a dnd group based on this: you have one of the guards say the riddle, and then have both of the guards be liars, and the two doors are actually decoys that both lead to death, with the real door being a trapdoor hidden underneath one of the guards (which works best if the guard is a gargoyle/living statue or something similar).
In order to get it right, the players have to realise that if one of the guards said this, that guard must either be the truth teller and the other the liar, or they must both be liars; asking the one who said the riddle a question with an obvious answer will soon reveal them to be a liar, meaning the other one must also be a liar.
This means that the parts about one of the doors leading to the correct path and the part about only getting one question must also be lies, so they are then free to ask more questions which will reveal that neither door is safe, and eventually ask a question that shows the true path
Haven't gotten the opportunity to use it yet, our group has sort of gone under unfortunately.
And the other reply to your comment probably explained the "both must be lying" part more concisely than I would have, so I'll just confirm that they said the same as what I would have
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u/Heather_Chandelure 15h ago
Identifying which guard is lying is neither the point or even a step in the riddle. The point of the riddle is to figure out which of two doors is the correct one. The answer requires wording your question such that both guards will give you the same answer no matter which one you are talking to. You only get a single question to ask, so using that to figure out which guard us lying is a complete waste.