The next main thing you’re going to want to, after cleaning the axles, is is to get some lube around those axles and potentially (read ‘A bit about the motor’ here, and blog post here) into the motor. You don’t want anything too sticky or oily, I’ve found CRC 556, Noxy, Power Lube with PTFE, or Multilube Gel the best, this is because you don’t want anything that’s just going to attract more dirt (you want something that will repel it – these ones all do that more or less). Also it is difficult to get to the innards of this motor (unless you drill out the rivet), so you need something very fine that can penetrate through a small crack (again CRC). Once you sprayed a little around the axles – using a straw nozzle attachment, spray a little along the top (again with the straw nozzle), and a little around the flywheel axle joints. Then give it a good rev up a push the clutch flap (that button normally presses) to get the lube moving into the motor and parts.
Any type of lube that you can spray on as a liquid then evaporates into a gel or tacky film-like grease (but does not attract dust), is pretty good for the outside of this motor around the gear rods and flywheel, as this type resists fling off at high speed and will likely last longer. Also probably pays to check that whatever you choose is ok for plastics, there are some nylon gears in there, and even though nylon is pretty stable with most lubes probably good idea to go with something that is non destructive on plastics. Synthetic lube that has penetration capability and is long lasting would be a good choice. Once you’ve got everything moving pretty quick, you may need to look into some of the other maintenance points related to counter-balancing and grip on smooth surfaces.