Quick snippet from 10/26. In case you ever wondered whether Akechi knows Mona talks all along... watch him here, and listen to him. At first he's on script—entirely in control even when he talks about how he was supposedly nearly murdered by himself. It's the same tone he uses on the news. He's gone over this speech a dozen times.
Then Morgana talks, and while Akechi does react, he's still acting. He's still on script, prepared and practiced. The portrait looks shocked, but the model is just standing there, playing detective....
... until Ann steps in with "our friend who taught us about the Metaverse":
He jumps back so fast I didn't have time to load the textbox, lol. "What do you MEAN you had a MAGIC CAT GUIDE, the FUCK??"
Of course he knew Mona talks. How does he expose himself, right away on 6/9?—he hears Mona talking about pancakes. He had to be close enough to hear Mona, the cat. So it's not Mona talking that shocks him, but the revelation that Joker and the rest had help, had a guide from the very beginning, when he did not.
And you can hear his voice change register at that moment. That careful, controlled, rehearsed tone goes out of the window. He talks faster, he pitches up, he's breathless, without a script. He is, in short, more real. And he immediately asks Mona a question:
He really hasn't solved that mystery; he really wants to know. In fact, he has to know—about the difference in their methods and his own, which he just can't figure out....
There's a little of that high-pitched breathiness when he talks about his awakening, too. I'd say that's pretty much how it happened way back when, and he's adapted the story a little. "I can't die here... I need to determine the truth"—of course he did. The same truth that his "sole interest is uncovering"—the truth about Shido and himself.
What about that image of the killer, standing in the entrance to Okumura's Palace? Well, sometimes people think this is a photo, but it's not—Akechi doesn't produce any more photos, he just continues with his story. So this is presumably what Akechi pictures in his mind at that moment. This is his self-image, God help him:
Lastly, here's an incredulous Akechi with a bonus Futaba glaring at him. Don't neglect the models—they really repay close examination, and the face animation is often incredibly detailed. And as for whether Akechi is lying or not at any given moment—it's often easier to tell than you think.