I know the lecture you are thinking of (I believe). In that lecture, the prof's statement that the laws of physics are reversible is grounded in what he explained, that each event is followed by a single event, such that:
- A -> B (allowed)
- C <- A -> B (not allowed)
Additionally, each event also only has one event prior to itself:
- B -> A (allowed)
- B -> A <- C (not allowed)
What follows from this is that the only acceptable sequence of events is:
In this case, the laws are reversible because, if in the original function, you could have event A, and know according to the laws that it would lead to event B, then C, you could reverse the laws, and given event C, know according to the reversed laws of physics that it would lead to event B, then A.
As for the lack of lost information, note that the universe he described is stroboscopic. In this case, each piece of 'information' is an event in the universe, and given that each event leads to another single event, the number of pieces of information is constant across time.