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I have a Lawn Boy 10515. It starts on the first or second pull each time. The engine continues to run perfectly. However, if I shut it off after it has been running, it won't restart. I discovered there is no spark after the engine is hot and shut down. After it cools it starts back up easily. Any ideas? I am stumped. Could it be as simple as a bad spark plug? I will appreciate any suggestions.

You probably need a new ignition module. Easy to replace. Source from Amazon or eBay.

Not uncommon for the coil to fail on these. Fortunately aftermarket replacements don't cost too much.