I've had two things along those lines on my L118 (that I no longer have).
First time, it was the gas cap had dust/debris caught up in the pin hole on the top of the cap that relieves vacuum in the gas tank itself, not allowing flow of fuel from the tank to the carb/engine. Was a very simple fix. Just take of gas cap and clean out little hole. If you take the cap off and try to start and it runs and keeps running, then that is your problem. Just clean out the little hole with a staple or something and move on.
Next time a couple years later, same problem again with running properly occurred. Tried the first fix. That wasn't the problem. Took it to a shop and they were able to easily determine that it was the vacuum pump (fuel pump) itself. They replace the vacuum pump and all was well. Sometimes, it's just old tubing on that same pump line that becomes too flexible and pinches on itself and won't draw properly. I never use ethanol containing gas anymore on any of my small equipment because the ethanol is not compatible with certain fuel lines and kind of weakens and dissolves them.
I'd guess your problem is probably one of these items. I hope so anyway because they are all easy fixes. You can take the line off the discharge side of the vacuum pump and run your starter and if you have gas flow out the discharge side of the pump, it is fine and is probably either the lines are weak and constricted, fuel filter needs changed, or the gas tank is vacuum locked as indicated first and won't allow the gas to flow to the pump. These pumps are not very strong.