How can they both explain it when one only tells lies?

The answer is stable because the liar will always say the bad door is safe and the truth teller will always say the safe door is safe, therefore the liar will always say that the truth teller will direct you to the danger door and the truth teller will tell you the same. I tried to add some self-reference to the question to make a paradoxical answer but can't see a wording that even causes something like "this statement is false", at least not one about which door to pick. Only ways I can think of start with the paradox right in the question. Like "If the other guard said, 'this statement is false', would you believe him?" Sucks someone downvoted just for asking questions to better understand this less than straightforward thing. I've always believed that if you think something is wrong, you should challenge it, because even if you are wrong, the resulting discussion can help you understand why your previous perspective was flawed, which might then cascade to other things you didn't realize you were also mistaken about.

Yes, but they did establish that one of the guards is no longer living and that giving barbarians riddles is dangerous for everyone involved.