This application does request true fullscreen through SDL's video API. There is an alternative option for a borderless window that covers the screen, but Lizard does not use this.
So, Lizard should not be able to do anything besides true fullscreen, and I have verified this to be working correctly on all the machines I have available to me. Lizard's fullscreen might look similar to the fake windowed fullscreen, because it requests the same resolution size as the desktop.
I can't say with 100% certainty that it's working correctly for you, there's always unexpected possibilities when it comes to video drivers and libraries like SDL, but to the extent that I have control of it in code, it's asking for true fullscreen.