Narration is an important tool in story-telling, and Tolkien was a master storyteller. I would even venture to say that his storytelling skills exceeded his skill at visual art, poetry, and novel-writing. And he obviously was quite decently skilled at those! But his storytelling is of the highest caliber.
Which is to say - Tolkien did not rely on 3rd person omniscient narration, nor did he choose a point of view character and stick to their perspective in the narration. Rather, he chose to narrate each scene from a particular character's point of view, and it was often the point of view of the least knowledgable person present in the scene. Pippin, not Gandalf, gives us our introduction to Minas Tirith. Gimli, who has never been to Rohan before, gives us the perspective of the Three Hunters. He cannot see what Legolas can see, so we the readers only see the riders when Gimli can see them, and rely on Legolas' report for what can be seen further away. We see Mordor through Sam's eyes, not Frodo's. Etc. This allows for the reader to discover things at the same time as the character, to be confused by things or surprised by things even if someone else in the scene knows more about what is going on. Sometimes, this is to preserve a 'surprise' - such as Aragorn's wedding to Arwen. But other times it is simply to immerse the reader fully in the story. Think about how Merry and Pippin's ordeal with the orcs is told - when the reader finds out what happened, versus when Gimli finds out what happened. It's rather complicated, and the choices that are made are at the aid of good storytelling.
So, as to the question of whether or not the narration "lies" - no, Tolkien does not usually pull a 'gotcha', where the narrator has claimed one thing, and then something different turns out to be true. But he does allow his characters to believe things that may not be the case, based on their limited knowledge/perspective. The entire gambit of Aragorn taking a small army to the Black Gate as a 'distraction' was based on the idea that, though he had a palantir, Sauron could not be certain that Aragorn didn't have the One Ring. He would see this action as a challenge from a new Ringlord.
There are places where characters supply misinformation. It can be rare, but it happens. Sometimes, it is merely hyperbole. Who is the oldest being alive during the Lord of the Rings? Is it Tom Bombadil? Treebeard? Someone else? A lot of characters are referred to with superlatives, and obviously most of them should only be getting a comparative. Every hot dog stand in Chicago sells the best Chicago-style hot dog (technically true - all supplied by the same place!) Other times, a character mispeaks. In "Shadow of the Past," Gandalf claims that it was clear from the start that Bilbo's magic ring was one of the great rings. That...cannot be the case, because the great rings all had a gem, and Bilbo's did not. It's either the One Ring or a lesser ring (with the chances being astronomically higher that it's the latter). Presumably Gandalf eventually came to the conclusion that it may be a great ring (after Bilbo's life had been preserved and he found it so hard to give it away), but he certainly didn't know that from the start and simply leave it in Bilbo's care for 60 years! He did not know for certain that Bilbo's Ring was the One Ring until he saw the writing on it in Frodo's fire 17 years after Bilbo left it behind. And thus, while he may have had suspicions, saying that it was clear all along is quite a bit of hindsight creeping into his telling of the story.
There is one clear example of misinformation given during the Council of Elrond. Gandalf repeats Gwaihir's report that the Men of Rohan pay a tribute of horses to Mordor. Boromir speaks up to dispute this claim, and is told that things may have changed since he came north. Aragorn, apparently, does not believe the claim either (as he states when they reach Rohan), but did not speak up during the council to gainsay Gandalf. When they arrive in Rohan, they find that Mordor has been sending orc raiding parties to steal horses from Rohan (particularly black horses), so horses are crossing the river, but Rohan is not paying tribute to Mordor. This distinction is important, and in fact may be one reason that Boromir did not wholly accept the information delivered in the Council of Elrond. When it came to something he knew about (how the people of Rohan value their horses), the Council was mistaken or willing to accept a dubious account. So when it came to something he knew little about (Rings of Power), he had some doubt that these elf lords and wizards knew what they were talking about. In other words...this piece of misinformation, delivered innocently enough at the time, serves a storytelling purpose and is not simply an incidental mistake.
Now, including misinformation or an unreliable narrator is a tricky thing to handle in storytelling. It's not always handled well. I haven't rewatched Rings of Power to see how they handled that yet. I am currently rewatching the Haunting of Hill House, and noticing lots of details in the storytelling that weren't apparent the first time through. Each character has a different perspective, and we start with the oldest brother, who knew the least about what really happened their last night in the house. There are some reveals that are not strictly believable based on later information, so that can feel like a 'cheat' - for instance, Luke's treehouse is shown in an early episode, and in the rewatch, I saw that it had a red door. So that detail helps to point to the truth, but...it's a treehouse. It's outside. The light is coming in through the slats in the walls. The reveal of its location feels fake, because we saw it...but we saw what the kids saw. That is a show that asks you to question what is real.
