If this happens, please pay close attention to the specific prize you won. In addition to infinite lives, you may also get a reward with infinite boosters (bombs, lightning, and stars). These are also activated automatically, and their timer is displayed in the overview window that appears before you start a level.
If you believe that you did receive infinite lives as a reward but do not see evidence that they have been activated, then please check the level overview window. It may well be that you actually received a reward of infinite boosters.
When you receive infinite lives, they appear in the top right corner of the screen in place of the standard life counter and are marked by an infinity symbol (∞). There is also a timer that indicates the amount of time left before your infinite lives run out. If you won infinite boosters, then the infinity symbol will appear in the level overview window near the icon of the corresponding booster.