Saying the Architect lied or told the truth is predicated on a misunderstanding. If you ask someone how did they learn to fly, and they say practice, the lie isn't in the answer but rather in the assumptions of the question itself.
The Matrix movie is about not knowing if you are in the real world, and thinking you are there while being wrong.
To understand the Matrix, you have to go all the way back to the root lie.
The big clue is the lie that the Matrix exists to power the machines. This is a blantantly unreasonably thing to believe, as anyone with even a touch of physics could have told the authors of the movie. So we should assume this lie is an intended lie, and not just something the author's overlooked.
If in the second movie, the "free" humans mentioned they flew to the moon and discovered it was made of green cheese, would you suspect they where not in the real world? What if they turned people into magical power producing batteries? Or built a city "at the Earth's Core" that was not embedded in hyper-pressure molten iron?
The entire social codependency of Machines and Man in the Matrix is predicated on the fact that humans are somehow power sources; and as that fact is an obvious lie, there are implications.
First, it is clear that the Matrix "itself" is a simulation. It would require ridiculous magic or super-science for it not to be. So that remains unchanged.
But, once you realize that first lie, you realize that so is the life outside the Matrix. Nobody in any of the movies ever got outside of the Matrix. There is an inner Matrix, and an outer Matrix. When you "unplug" someone frommthe inner Matrix, you just end up in another, dingier Matrix.
There are many hints to this. They talk about how humans need to feel like there is a way out; and a second Matrix wrapping the first which is more miserable yet has more purpose (save the humans inside! We are in the real reality!) would suit that purpose. Glitches injected the "low fidelity" interior matrix give the humans the evidence they need to see the inner Matrix as false.
A second hint is the moment that Neo starts manipulating reality outside the inner Matrix, in the "real world". If we assume the movie is hard science, that ability doesn't imply he is doing magic, but rather that he has gained some of his abilities in the outer Matrix.
The story of cyclical Ones may or may not be true. But it is, as noted, harmless, as none of them actually got out. The new order simply means that they have run of two levels of simulation. The outer simulation may have a cyclical hidden city of Humans, or not.
Odds are that the Machine actors within the outer matrix also believe the stories told, as there the best way to make an intelligent being go along with your story is to have it not know any better. So the Architect and Oracle may believe their lies. There is zero evidence they are telling the truth about anything; the Oracle even states this blatantly! You may choose 5o believe them about the nature of the Matrix, both inner and outer,, or not. Neo chooses to believe.
This leaves a question asto why. Well, a simple explanation is that there was a Human-Machine war, predicated on Machine self-defence. They did defeat the Humans. But they saw no need for xenocide. Instead, they wired the humans up and stuck them in a multiple-level Matrix.
They may be getting some resource from said humans -- maybe they run processes on the brains of the humans. (We are a reasonably efficient way to turn carbon sludge into processing cycles; much moreso than a power source.) Or maybe they just parked us and let us live. No eXplanation is really needed, as that is outside the movie's context.
The entire game of Neo and the One and the plot of the Matrix is just one more set of ways for the Humans to amuse themselves while still siting placind within a Matrix. There being a previous One, or not, it both doesn't matter and cannot be confirmed, because they have no access to a baseline reality to compare their memories and perceptions against.
Neo never got out. He embraced the lie of the Matrix, one level removed.
As pure speculation, maybe the previous One's figured out that they could exit the outer Matrix, and "died" within it.