DON'T CUT THEM!!!!!
The lids don't come off the way you might think, but they are designed to be removed so the tray portion can be stored in a rolling chest.
Look at the case, opposite of the lid side, while it's open- you'll notice that the hinges are attached to the lid on the same side (both on the left or both on the right of the hinges from the tray part). If you hold the bottom tray part in place and push the lid sideways (left or right) towards the direction of the hinge section connected to the lid, it will pop off. There's just a little plastic detent keeping the lid on.
I had a set in my box for a few years and this was a great feature. I ended up selling it because the ratchets auto reversed almost every time I used them and it was nice to be able to put the lid back on.