Lencioni is talking about a specific kind of trust here, and it is worth being precise, because this is where most people misread the model.
He does not mean predictive trust, the sort where you know a colleague will deliver the report on Thursday because they always do. He means vulnerability-based trust. Being willing to say "I got that wrong", "I do not understand this" or "I need help" without calculating what it will cost you.
What it looks like in practice
People come to meetings with their positions already worked out. Mistakes get quietly absorbed rather than raised. There is a lot of careful language. You will hear "just to be clear, I did flag this in April" more often than you should.
What actually shifts it
Trust is built in small, repeated, fairly boring moments, not in a single away day with a raft-building exercise. Coffee before the meeting starts. Someone senior saying "I have no idea, what do you think" and meaning it. Consistency over time, so people learn you are the same person on a bad Tuesday as you are on a good Friday.
The single fastest accelerator we have seen is giving a team a shared language for how they differ. When people can say "I process this internally before I speak, so give me a minute" and everyone understands what that means, a whole layer of misreading each other disappears. That is a large part of why we use Insights Discovery in teamwork. It is not the model itself that does the work, it is that the model gives people permission to explain themselves and how they feel in this team