how do I fix a broken blade lock?
First, confirm the saw is unplugged. Then hold the guard out of the way with tape. Place a box-end wrench onto the nut. Position everything so you can tap smartly on the wrench with a hammer or metal bar. The inertia/mass of the motor will delay the shaft turning and, with luck, the nut will start to loosen. Remember it is right hand thread.
You could also use a cordless impact driver. Put a 3/8" square adapter into the hex chuck, then an impact socket. Use short bursts of the gun. I have used the tapping technique many times over the years.