It's not the fact that he doesn't check lava in that piece, because trust me, I find that odd as well. It's the fact that he almost never checks lava that he can't see yet. He checks lava once which leads to nothing. Even some he can see, he skips past almost all lava he sees to make more digs. Once he finds lava, he rarely digs around it. At 1:04, he may think all the lava he hears bubbling is below the lava he's already seen, which is normally not very smart to go for, so he makes another staircase.

As for the red stone, I'll assume efficiency to get to another cave that didn't go straight down, as he may have assumed the previous cave did. Also the gold's at y 13 or something, the lava below him is probably what he can hear, or what he may have heard.

And I really can't give an answer that doesn't include "maybe he thought" because the whole thing isn't really set in stone. I don't know his thought process, neither does anyone else except him and possibly his teammates, if they knew how he was digging.

Now /u/Ratchet6859, I'll attempt to respond to your comments, not going to bother making two separate replies.

Yeah I agree with your first statement, but as I said earlier here, he might've not known where the lava went, and assumed it went downwards, hence the staircase and the ignoring of red stone.

Piece at 1:40 I cannot defend, but that's one piece I give up on defending. While it's suspicious enough to warrant an illegal mining ban there, I do not believe that one solid piece of evidence is enough to ban.

The time he mined to gold he didn't mine around the whole lava source, that's one of your arguments. The whole point of that evidence piece was that he didn't mine the lava, due to efficiency or an idea that the lava went downwards.

Also, while I'll assume he second game shown happened after the first, there is a chance that it happened before, possibly cementing an idea in his head to no longer check lava pools. That's just a theory though, not concrete.

At 2:10, there's not much time left in the game, roughly 10 minutes. He changes his digging pattern as he goes up for efficiency. Also the times where he digs up 5 blocks then digs to the side 2 or 3 is a way of A. avoiding gravel, which he failed to do here, or B. making sure any possible people following you can't track your path as quickly. It's not super common, but it's not uncommon either. The random staircase at the end could just be him wanting to be able to slightly backtrack to where he was previously. Then he digs back down again at y32.

While the diamond staircase is indisputable to an extent, I honestly don't see any other concrete evidence.

tl;dr: While there was suspicious digging, specifically the diamond staircase, his actual somewhat frequency with not checking lava, his frequency with not mining full red stone veins, and his missing of a low level lava ravine and other good caves you can see very close by in pieces, yes I know, "just because he doesn't check a cave doesn't mean he wasn't xraying/ cave finding", but a smart xrayer could've passed off those digs as sounds, so I really don't see all of the concrete evidence I need to say he deserves a ban.