If I've understood correctly here, you are getting a complete new LM carby?
If that's the case, I would suggest we see how that goes, if there is still a performance issue after that, then it's time to isolate the decompresser, and do a compression test.
In the meantime, drain and clean out the fuel tank, and remove the tap to clean the filter and make sure the lines are free of blockage.
The check the vacuum lines to the Governor and decompresser (these are the other 2 pieces of fuel line coming from the carby) to make sure they are clear (with the Governor line, make sure you can blow fairly freely through it, while it is still on the engine, with the decompresser one (goes to the funny 'mushroom') remove the line entirely to check it is clear)
as you are replacing the snorkel, you wont need to worry about cleaning that before the new carby arrives.
If the mower will be waiting with the carby off, make sure to cover the intake port, to protect the engine from rust.
