Did you get just one bill after the teenager had the LTR? Or did they keep coming week after week? Depending on where you are in the cycle, you can still get a bill when you purchase the No Bills Lifetime Reward because it was already in the works. But you won't get bills after that.
It doesn't matter which of the household members buys the No Bills LTR, but when that Sim moves or dies, the LTR is gone and someone else will have to buy it again to keep the bills from starting back up again.