Well done but not over yet Marc.
Grab a car of dry spray lubricant.
Lithium Chassis grease is the most cost effective.
Make sure it has a long tube nozel with the can.
Blow down the mower with compressed air & a long air duster ( if you have one ) or even a leaf blower.
Get the mower up high and everywhere that 2 pieces of metal rub, run or screw into each other give it a saturation spray.
The penetrating oil is good to break rusty things free but most have very little in the way of long term corrosion resistance.