Peerless 801 transaxle. They are shipped with 32oz of bentonite grease in them. The grease tends to dry up over the years and cause shifting problems. The shift fork and de-tent sector are made of stamped steel and can bend once the grease dries up and the reverse chain can get stiff and break.
If your mowers still shift nice and smooth without having to force them into gears I would not worry about them to much.
Here is the OEM Bentonite Grease that is made for them. I would probably put 1/2 a bottle in each if you can squeeze that much in them.
It's Actually a little cheaper on amazon if you have Amazon Prime. https://www.amazon.com/GENUINE-OEM-TECUMSEH-PARTS-788067C/dp/B008TSZ98I
Here is a pic of a new peerless 801 transaxle. You can see the yellow fill plug on it. The fill plug might be covered by the front mounting bracket and the big pulley on the 108 and 111 so the trans will need to be removed to fill put lube in them.
You could always drill a hole in the case somewhere near the Back Left Corner of the case and install a grease zerk and pump some light weight grease in them. Back Left corner is a hollow spot next to the bull gear and the bull gear will sling the grease around once you start moving. I would use a Lighter weight grease so that it gets slung around in the case by the gears.
Back Right corner has a hollow spot and an axle support in the inside of the case. Don't drill there because it will just fill that empty cavity.
Here I marked a good spot to drill if you want to install a grease zerk in the case.