Belay devices like the Lifeguard and Gri-Gri were not made to be used the way we use them here. Basically for the reason you just learned. So you need to look at backing up the rappel with an autoblock. The lifeguard becomes your rappel device clipped on your bridge, which replaces the more typical ATC or figure eight device, etc you'll see in most videos on rappelling. The autoblock is a low friction prusik on the tag end of the rope where you would hold it with your strong hand. You clip the autoblock lower than the rappel device, usually 18" - 20" or so below the rappel device. I clip it in at my linesmans loop, some will clip it to a leg strap.
Once the autoblock is properly tensioned you can flip the lever on the lifegard to release the cam off the rope and the autoblock will keep you in place. If you apply light pressure at the top of the autoblock prusik with your other hand while holding the lifeguard lever open it will slip and you will descend. Take the pressure off the prusik and you stop,
Once you get the feel of that at at low height you'll understand what is going on there and you can just hold the lifeguard lever wide open and manage the descent by applying and releasing pressure on the autoblock. It will take some practice, but once you get it its a safer and more manageable way to decend without burning up the rope or your hand.
Meant to add too that you can hold the lifeguard lever at different pressures so the autoblock doesn't have to work so hard too. Its something you have to do yourself, but its easy.