Why does a lawnmower start and the die?

First make sure that the air filter is clean. If that is good then the carburetor is dirty. It is getting enough fuel to start, but isn't able to deliver the amount necessary to keep it running. The carb needs a good cleaning. The best way is to take it off of the mower and take off the float bowl and use a carb cleaner to spray it out really good. Also you need to get a really thin piece of wire and clean out the passages of the carb. I hope this helps.