Does it start and run okay while it's running? And then just dies after a couple of seconds?
No it does not run, it just dies after a few seconds.
I think your engine model is actually 125K02-0243-E1. I've linked to a breakdown of the carburetor below:
Although it would probably be a good idea to take it off and do a full cleaning, let's see if we can't get you started with a minor cleaning.
Pinch the fuel line shut to stop the fuel and have a container ready to catch the extra. Take off the bowl of the carburetor and look to see if there's any sediment in there. Clean it out. Take some spray carb cleaner and clean the small holes in the bowl nut. This is your high speed jet. Use some soft wire like from a bread tie to probe the passages t mke sure they're clean. Spray some carb cleaner up the center leg of the carb where the bowl nut threads into and also down the throat of the carburetor by removing the air cleaner.
Let me know and we'll continue.
I'm posting this as an answer, but let's make sure you're up and running before you accept.
Thank you for the accept. Here's a bit of followup infor in case you need to do a full cleaning:
Take pictures or at least make a drawing of where all the linkages, gaskets, and component parts go. Correct reassembly is critical. Clean every part with carburetor cleaner (soak is better than spray) and blow out all the small holes and passageways with compressed air or use soft tag wire to make sure they're not blocked, them blow through them. Do not get carburetor cleaner on the non-metallic parts since it will cause them to decompose and futher plug the carburetor. Remove the carb cleaner from the metal parts by washing them in warm, soapy water then rinsing with clean water. Dry them thoroughly before reassembling using your pictures or drawings as a guide.
Best of success in all you do,