I am sending you an article from homeguides.sfgate.com but they don't mention the first thing I would suspect until the end of the article, which is the coil.
It can be puzzling when a lawn mower starts easily and runs fine for a few hours, only to stop with no warning. This sudden shutdown can be caused by an overheating engine. Reasons for an engine to overheat and shut down include debris clogging the area around the engine, low coolant levels, a problem with the oil, or an engine mechanical breakdown.
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Buildup of grass, twigs, and other debris that block air from reaching the engine can quickly lead to an overheating lawn mower. Debris in the engine cooling fans, engine shroud, air intake screen, grille and/or side panels prevent air circulation that would normally keep the engine cool. If the engine gets too hot, it will shut down and may be damaged. In some cases, the buildup of dry grass may catch on fire. Remove grass clippings from the engine area regularly to prevent this problem.
Low Coolant or Oil
Some lawn mowers use liquid engine coolant to keep the engine from overheating, much in the same way as a car. For these mowers, check the engine coolant before each use and refill as necessary. Engines also require lubrication from oil to prevent overheating. Check the oil levels when the engine is turned off and the mower is resting on a level surface. If the level is below the "full" mark, add fresh oil. Ideally, check oil levels after every 20 hours of use, or each time you use the mower.
If a mower dies when the area around the engine is clean and oil levels are correct, there may be a problem with the fasteners in the engine. Begin by checking the carburetor mounting bolts and the bolts located where the intake manifold and engine block attach. Popping or puffing noises near the engine head may indicate that the head bolts are not tightened far enough. If noises seem to be coming from the exhaust system, check the exhaust valve. Tightening any of these fasteners that seem loose may solve the problem.
Certain problems that cause a lawn mower engine to overheat and shut down require more extensive maintenance to correct. Routinely check engine parts, such as shrouds and cooling fins, for damage and replace as needed. If the engine will not restart until it cools down, the exhaust valve or valve seat may need to be replaced. The condenser and engine coil can also cause overheating if they start to go bad. Maintenance on these systems can be performed at home by removing and disassembling the engine to replace damaged parts, or by taking the mower to a qualified service technician."
I hope that helps! :)