This is a case of ketiv and qere.
The ketiv (written text) has לא which is usually a particle of negation:
לך אמר לא חיה תחיה
Go say, "You will surely not live."
The qere (read version) corrects this to its homophone לו which means "to him":
לֵ֥ךְ אֱמָר־ל֖וֹ חָיֹ֣ה תִֽחְיֶ֑ה
Go say to him, "You will surely live."
This isn't strange, because there are many times where the written text has לא where it means to "him" and the qere routinely corrects this to the standard orthography of לו (e.g. Leviticus 25:30). Therefore the ketiv doesn't necessitate reading it as a particle of negation rather than "to him." The story here reads fluidly if we take the meaning "say to him" because that is exactly what happens: Hazael says Ben Hadad will live, and then Ben Hadad dies (8:14).
However, the fact that this spelling was chosen here by the ketiv might be especially significant. Since the words were homophones, Elisha's statement was ambiguous as to whether he was saying Ben Hadad would die or not, and therefore he didn't lie. This might have been an intended nuance of the story from the beginning, just like Abraham used a technicality to avoid lying about Sarai being his sister (Genesis 20:12). Elisha himself made a similarly ambiguous statement earlier (2 Kings 6:19): he tells the blinded soldiers searching for him to follow him, and he will lead them to the man they seek. By following him, they are of course being led to him, though they are unaware of this.
This unusual spelling could have even been the work of an editor. There is precedent for this in Greek commentators who were troubled by a passage in the Iliad in which Zeus seems to lie. Hippias of Thasos (as quoted by Aristotle, Poetics 1461a; see footnote 7) solves this "Homeric problem" by changing the accent of one word so that Zeus isn't the one lying. The same could have been the case here, where a change of one letter saves Elisha from having told a lie. Whether it was the author or the editor, someone who didn't want to portray Elisha as a liar could have used this spelling here to highlight the ambiguity in his words.