I have a teammate who occasionally lies, or exaggerates
questionably, about our team's progress...
How should I handle this?
The context is important here, so as always, it depends. A lot depends on department and company culture, and the relative positions of the individuals involved.
I never lie. And I never cover up for the lies of another. On the other hand I don't feel it is my responsibility to point out the lies or exaggerations of others, unless there is a clear and direct connection to me.
If I were the team lead, and someone on my team were lying about our progress, I would immediately correct it. I feel that the Lead (or Supervisor, Manager, etc) is directly responsible for reporting the team's progress and is the de facto voice of the team. The view of the team's progress should come through the leader.
In your situation, if a teammate or peer of mine exaggerates about our common team, I wouldn't interrupt. However, if I were asked my opinion about our progress, I would always give my opinion - even if it directly contradicted my teammate's opinion.
I might speak to my teammate privately after the incident, and ask about the progress report he/she gave. And I would likely try to leave her/him with the impression that if the superior had asked my opinion on the topic, I wouldn't have responded the same way. This wouldn't be delivered as a threat, just as a heads-up.