Lawn mowers can take 2 stroke or 4 stroke oil depending on the type of engine. If unsure contact your lawn mower provider.
30w, 10-30w or 10-40w
You do realize you can use any oil in your White lawnmower and do not have to purchase White oil. White does not even manufacture oil and their oil is made by someone else. In fact White does even manufacture lawnmowers. Their lawnmowers are made by MTD. Purchase any name brand oil in the correct weight for your mower as recommended by the engine manufacturer. I do highly recommend you use a synthetic oil for any air cooled engine.
22hp Briggs lawnmowers
Non-detergent oil, such as SAE 30, is not used in modern passenger vehicle engines. It is still used in some gasoline engines such as lawnmowers.
You can use any kind of 10w-40 oil for a nighthawk
They did not have enough oil for their lawnmowers so the economy went way down.
Baby oil
Most use Synthetic Oil.
Rocket oil
The answer is in the question, because they use Gas.
That depends entirely on the engine. All of my newer Briggs and Stratton engines recommend single weight engine oil in the sump, 30 weight for summer. Use detergent motor with at least an API designation of SG (SH, SJ) and you should be okay. Some lawnmowers use 2 cycle engines which require a special 2 cycle oil mixed with the gasoline. For a new lawnmower use the oil that the manufacturer recommends to maintain your warranty. If you want a more specific recommendation you will need to provide specific information about the engine and its age.
They use the oil God gave them in their oil glands.