Yeah, I've played this and it's a lot of fun! I do have a spin on the game.
Everything is the same as you said except I have the listeners place "bets" on their answers. For example, when the time comes and the listeners have to say if it's true or a lie, then they have to put their "money" where their mouth is and bet whatever you are playing with (ie. scraps of paper, fake money, pennies, cookies, etc...). That motivates them to listen very carefully to the student saying their lie/truth.
You can also take it one step further and allow the listeners to ask Yes or No questions about the statement, but that would be for a fairly high level class.