The lawn tractor is very important for the up keep of the outside of the home. I have found a similar question that might help you in getting the equipment up and running again. The other thing that i would suggest is to place the model number on to this thread so that way the expert can provide specific information upon your lawn tractor.
This type of problem will almost always be related to bad/old fuel or a problem within the carburetor resulting from old fuel being left in the carburetor for extended periods of time.
I found a video that gives a good demonstration on how to clean a carburetor and you may want to give it a watch before you take yours apart. The machine in the video may not be exactly like your machine, but the theory will be the same.