Most children reach this stage early -- and at three years of age, they can, in fact, lie. It's a natural progression, which parents will then spend time trying to curb, and it's positive precisely because it indicates developmental growth. It is, however, hard to appreciate this in a cheerful way when your own child is lying to you, but it's the silver lining on the cloud.
My oldest son didn't fully develop the ability to lie until he was seven years old. But the slow development of theory of mind did occur.
(If it makes anyone feel any better, I didn't know the phrase "theory of mind" until my son was well into six years old, because that's when we received the first solid diagnosis. I did understand that he wasn't aware that what he knew was not universally known, but that was acute, parental-paranoid observation.)
My son's grade one teacher had managed to create an environment that was consistent enough that he felt more or less safe. He found school rules confusing; he didn't understand why the children (he often used the phrase "the children" at that age) had to, for instance, walk quietly back to their classroom when in the halls between the library or the gym; when I pointed out that the noise was disruptive, I had to explain why (the children in other classes won't be able to hear their teacher, which spawned a different set of questions). He didn't understand why, if he was being quiet at the back of the room, he had to come and sit in the class circle and be quiet there, etc.
But he was comfortable with his teacher, and with most of his classmates. There were exceptions, and it was difficult. Some of the children in particular were physically violent -- in part because he was socially completely unaware of ways to integrate with that group, and in part because they were the loudest children present, and he was drawn to shouting, laughter, and high energy physical motion. There were a lot of kids in his class who actually liked him -- but he failed to notice most of them in day-to-day activities because they weren't loud enough.
As you can imagine, this can colour the impression a class leaves. His teacher was aware of the difficulty, but also aware of the fact that my son would run into it, time and again. So I explained the why of his constant approach, and she tried to keep an eye out and mitigate the inevitable consequences, lending new weight to the phrase "this will all end in tears".
She attempted, in class, to put him into groups with children who were more empathic and less hierarchical. One of these groups was the MSI group. (I'm embarrassed to say I no longer remember what the initials actually stood for; the first two were Math and Science, but I can't for the life of me remember what I was.) In practical terms, MSI was used to encourage group participation in projects.
This was done in grade one, by the teacher; the grade two teacher thought it insanely ambitious because she expected it would fall apart in pointless squabbles. I firmly believe, were it not for the particular grade one teacher we had, this would have been true. But in the main, the groups formed. During the building block session of the MSI afternoon activities, the children had to discuss a project, decide on a project and build that project.
I've mentioned that my son's teacher liked to resolve difficulties in her classroom on her own; only when she'd reached a point where she felt she was missing something, or couldn't correctly interpret certain behaviour, would she ask to speak with parents. One day, when I picked up my son, she asked to speak to me.
It seems that for several weeks -- weeks, I think it was six -- he'd been involved in MSI with two other children. The two, as the teacher pointed out, were the nicest kids in the class -- a boy and a girl. At the end of every session, he would inexplicably destroy the work of the class, to the point where the other two were -- completely understandably -- getting frustrated.
She was accustomed at this point -- the entire class was -- to his accidental acts of destruction, because at a certain point in the afternoon, my son was completely unaware of his environment; he could walk into doors, collide with desks, trip over chairs, etc. So the whole class knew enough to guide him away from anything fragile (often by standing in front of it).
This case, however, was not the same. He was deliberately destroying things. I asked a couple of questions, and then said, "I think I know what the problem is. Let me talk to him tonight, and I'll speak to you in the morning."
So, we went home. My son was, and is, a reasonable child. Destroying the project was not a reasonable act -- in our eyes. But it was completely consistent with an act of anger and resentment, even if he had nothing to resent on the surface of things.
What I suspected was that the difficulty started with the "discussion and choice" phase. By the building phase, he was already bitterly upset. I was right. I also believed that the teacher had, as she said, given him to the group with the two nicest children in the class.
And here's what was happening. The girl would start the discussion phase by saying, "I would like to build a castle." The other boy, having no set preference himself, would agree because a castle sounded good. My son? He would say nothing. When I finally managed to get him to speak about this (mostly by attempting to talk about my own grade one experiences, because matching experiences were often the only way to bring him out, even if they had to be improvised), he was upset.
Because they didn't care what he wanted to build. He felt very much that the only thing that mattered to them was what they wanted, and that he was being forced to go along with it.
You can see the problem immediately, here. I waited for a few minutes while he tearfully explained his hurt, and then said, "did you tell them what you wanted to build?" he blinked. His theory of mind was not in place, yet; the idea that what he wanted had to be communicated had not occurred to him. At all.
He also didn't entirely believe me. But he knew I wouldn't lie to him. So I expanded. I explained that when the little girl said "I would like to build a castle", she wasn't saying "so that's what you have to do whether you like it or not" in silence--or at all. Discussions can open with "what would you like to do", but there's a decent chance that she did say that, at a time when he was distracted by the building blocks themselves.
I explained that she was waiting for the other two children in the group to state what their preferences were, so that they could all then discuss them and choose one. If she wanted to build a castle, and my son said, "I would like to build a train-wreck", she wouldn't be angry or ignore him. But if he said nothing, she would assume that he accepted the idea of building the castle.
He really did ask me to explain this five times, and when he was certain he understood my claims, he went away to think about it.
I'm not kidding--he really was hesitant about it. He couldn't make sense of what I'd said, because to him, words were optional, or even worse, pointless. This would be the lack of theory of mind.
I then talked to the teacher in the morning to tell her what was causing the difficulty, and she was almost baffled by it; she could accept that it was true, but it was not an explanation that had occurred to her. She asked me to explain things to my son, and I said I would try--but I also knew, from bitter experience, that in this case, it would be like trying to teach him calculus before he'd learned multiplication; he was trying to grasp things, but they were not yet in reach.
But the next MSI afternoon was the first one in which my son didn't cause difficulty.
I asked him about it on the way home. At six years of age, he couldn't bring himself to ask for anything to which No would be a possible, logical answer; not at home, and certainly not outside of it. But he did make comments and suggestions in a roundabout way, to confirm for himself the truth of what I'd told him. To his great surprise, he understood from the reaction of the other two kids that I was right, even though what I'd said made little sense to him. He was in a much, much happier mood on the way home that day, because the afternoon was like an epiphany for him.
People weren't ignoring him or attempting to impose their desires over his against his will. They didn't know. This was logical construct on his part; it would be another year before he was able to automatically grasp this. Once he realized he did have some say, he was happy enough to give it away, because the greater difficulty -- of asking for something directly -- was one he couldn't force himself to overcome at that age.
This was the start of his slow development of that very necessary theory of mind.
It's my suspicion that full-blown autistics have never developed it.