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.
I took a look at my notes and code again and there is one caveat to that previous statement: if fullscreen is being applied on your second monitor on a two monitor system, it is forced to use the fake fullscreen overlay for that monitor. So the solution could possibly to change your primary monitor setting if it's a two-screen setup.
Alright, nevermind, you're absolutely right. I did update drivers recently, and now I have stuttering in all games, period, no matter the display method. I just assumed Lizard did windowed fullscreen because it kinda looks like it and I got stuttering, but now I got stuttering everywhere :P There's probably nothing wrong in the game, but with my setup.