The rest of the October list, which is short:
Change the oil before storage, not after. Used oil carries acidic combustion products, and leaving it sitting on the internals for six months is the avoidable part. Fresh oil going into storage is the correct order and most people do it backwards.
Take the spark plug out, put a small amount of oil in the cylinder, and pull it over slowly a few times to coat the bore. Then put the plug back. Two minutes, and it prevents surface rust in the cylinder.
Clean the deck and the air filter. Wet grass left on a mower deck holds moisture against metal all winter.
Battery on a maintainer if it has one, or off the machine and topped up occasionally.
And the buying decision that ends this permanently for the machines you use rarely: ethanol-free fuel if it is available where you are. It costs more and it stores far better, and for a generator that sits eleven months a year it is worth it on its own.
On your mower specifically, since it has been cleaned three times: check the fuel tap actually shuts off. A tap that weeps keeps refilling the bowl from a tank of ageing fuel all winter, which defeats running it dry and would explain why it is always that machine.