Why does my lawn mower stall?

Probably a plugged filter or screen in the gas tank.

Also clean the gas filter. It may be in the carb inlet or the gas tank outlet, or in the gas tank itself. You could try giving it a little extra gas when it starts to die either by choking it a bit or squeezing the primer bulb, if you have one. If it improves then you will know it's a gas supply problem

And then it could be a bad coil. I have a chipper shredder that from day one wouldn't restart when it was hot from running until it had set for a couple of hours. Kept getting worse until it finally wouldn't start at all and found a bad coil and rplaced it. Now it starts every time, cold or hot.

It's obviously overheating, and so a filter somewhere is blocked, or you haven't any oil in it.

Simply mow faster, so that you get all the grass cut within 45 minutes.

It could be a dirty gas cap. There are little holes in it to let air into the tank as the gas flows out. If the holes are plugged up then eventually the gas will stop flowing out of the tank. A simple test for this is to take the gas cap off as soon as the engine starts sputtering. Of course, if it smooths out then you know the cap is the problem.

You say it won't restart until it cools down. It could be that it takes awhile for air to seep back into the tank so gas can flow out again. The holes in the cap may be mostly plugged but not totally plugged.

When did you last clean it? Check the air filter and give the carburetor a clean. While you're at it check the fuel tank for crud that may have gotten in.