Actually though, I do seem to remember a legal precedent that it is not illegal for a candidate to lie.
However one of the articles of impeachment prepared against Nixon, was for "lying to the public". It of course never got as far as a Senate trial, due to Nixon's resignation, so it's never been proven out. I doubt "lying to the public" would have taken down Nixon, and there's no way I can see it doing so here with Trump.
The only thing I could think of here, is Mueller trying to use the Twitter account as a piece of corroborating evidence to other evidence he has. For example, if Mueller were to go after Trump for Obstructing in the AF-1 letter composed to obfuscate the Trump Towers Russian meeting.
If Mueller were to establish Trump had prior knowledge of the meeting, and if Mueller had witnesses on the plane while Trump composed the letter, say Hope Hicks or someone else, then I could see him bringing-in Tweets where he further obfuscated the truth.
Now I'm not saying this is indeed what happened, nor am I saying this is a winning technique. But I am saying I can envision scenarios where the Tweeting might possibly be considered evidential.