For me, "completely lost sense of time" sounds almost psychotic. "Completely lost track of time" is a way of saying that one was so focused that one did not realize how much time had passed.
That's what I meant. Imagine someone without a clock in a room with no windows, like some prisoners. After a while, they could easily lose all sense of time.
I can't speak to their thought process. If you didn't realize several hours had passed or that it was later than you thought, then you "lost track of the time."
It's almost impossible to pin down meaning exactly, so there will be differences in interpretation. I would not use it as a synonym for lose track of time. For me, lose all sense of time is a greater temporal confusion.