To make bucket lids into "easy-lids" I hand-marked 3 tabs to save (about 1-1.5" long each). Then the table saw was setup to do the "along-the-arc" cuts. I rolled the lid down onto the saw blade to cut at the marked line, then rotated it to cut up to the other marked tab location.
Then the (6) tab edges were cut on a bandsaw.
IMPORTANT NOTE: Both of these cuts have a tendency for the lid to grab which can be dangerous. For the table saw cuts, stand off to the other side of the fence so if/when a lid gets caught it does not get thrown into you. A fine toothed blade is better. Also when rolling the lid into the saw, it's a finger-remover waiting to happen if you're not careful. (yes, I still have 10 complete fingers)
Come to think of it, if you're not a table saw guy (I use my table saw extensively) then you may not want to try this.
I tried the utility knife for about 2 seconds and gave up. My wrists are trashed though, maybe it will work for you if you have fully functional wrists.
2010 10 taps, turkey fryer, loads of family fun.
2011 Made a 2x8, boiled 3500 gallons of sap.
2012 800-ish taps, new filter press, new friends