Tecumseh push mowers have a plunger pump similar to the pump soap jugs in your home. This pumped oil to the top camshaft and the top crankshaft bearing. There was a hole that shot oil to the connecting rod bearing. This system actually worked pretty good.

Briggs, Honda, and most of the others used a splash system that worked very well. Kawasaki uses a pump to supply oil.

Most of the large two cylinder engines use full pressure lube with oil filter. Some of the Briggs single cylinder have an oil pump and oil filter that filters the oil in the crankcase, but uses splash lube for bearings.
The higher priced single cylinder Briggs does have full pressure lubrication.

the question on engine life comes up occasionally. Briggs used to test their engines to 1000 hours in their testing facility. In residential service, the engine life depends on owner maintenance. Most owners maintain for about ten years - then they buy a new mower.

que sera sera

If you have one of the cheaper push mowers, without oil pump and filter, then you should change the oil much more frequently, and also make sure you always have a good air filter in place.

Life of any engine is directly tied to care and usage. While changing oil is certainly critical, I think air filter service is even more important. Use of a fuel stabilizer and light but consistent use of a solvent oil like Marvel mystery Oil (1 oz/gal for 4-cycle, 2 oz/gal for 2-cycle) can prevent carb trouble and excess carbon build-up. Ideally you would use a synthetic engine oil designed for air-cooled service and change it at least yearly. I have had B&S 3.5 HP engines that outlasted two or three mower decks. One I bought in 1971 had already done that by the time I gave it to a cousin who still uses it. Another one I bought in 1990 is still in use at my older brother's house. I actually have never experienced mower engine failure or removal from service for any cause. My current mowers, one with a Tecumseh 195cc and the other with a Honda commercial 190cc are ten and six years old respectively. I typically never replace spark plugs. I eventually had to replace the plug on the B&S my brother has because another relative had it before him and he insisted on using stale gas in it that he had stored for 'Y2K' and never used in the car. I probably would look at the plug after twenty years, or sooner if the engine was not running right.
So really there is no upper limit to mower engine life under ideal conditions. In the real world populated mostly by idiots, mower engine life can be as short as 15 seconds when they start a new mower without putting oil in the crankcase.