Greetings! Sorry for seeing this a bit late. Was, of all things, doing some mowing yesterday afternoon!
What is the model of the LawnBoy that you have? Depending on the type of carb, the cause could be in different places but is the same problem. A blocked passage.
No, a new carb won't be necessary. What I would suggest is taking the carb off and getting a can of spray cleaner, such as Gumout or a similar brand. Carefully disassemble the carb, cleaning the different metal parts as they are removed, such as the sediment bowl (if metal), with cleaner. When done taking it apart, spray all passages with cleaner and push a very fine wire (stereo speaker wire works for me) thru the passages to clean them out. You could also soak the carb in cleaner over night, but I have never found that necessary.
Now, if you have a LB with the Tecumseh 4 cycle engine, the culprit is likely some small fuel passages that are barely visible. You probably will not have to take off the carb to fix this issue. Take off the small bolt that holds the sediment bowl on. It is brass, and actually contains 1 to 3 extremely tiny jets near the head of this bolt. You may not even be able to see them at first. Clean out the inside of this little bolt and use that fine piece of wire to clean the blockage out of those extremely tiny fuel passages. Put it back together and you should be able to get it to run at this time. I would suggest some fuel line cleaner, such as liquid Gumout or SeaFoam (very good!) in the tank to help clean out the rest of the fuel system. An ounce or 2 will fix it right up.
Any other issues, or if you could supply the model of mower, just let us know! Good Luck!