While some of the answers given here raise valid points, they do not specifically answer the question. Four stroke engines use a splash type or a pump based lubrication system. But most of the two stroke engines can't use such dedicated lubrication systems because in two stroke engines the inlet and outlet (exhaust) bores are on the sidewalls of the cylinder. So if a splash type or pump based lubrication systems as used in four stroke engines would be used in two stroke engines then the lubricating oil may enter these bores and block them. Moreover, unlike four stroke engines in which there is an oil sump inside the crank-case, the crank-case in two stroke engines is used for pumping and circulating air-fuel mixture to the combustion chamber (thus making it unusable for storing lubricating oil ). So, instead of using a dedicated lubrication system as in four stroke engines, most of the two stroke engines use a lubricant oil mixed with fuel so that the wear of piston and cylinder liner can be minimised. I hope this answers your question.

In the two-stroke engine, the engine oil in the mixture tracks around the piston rings for lubrication {by gravity};whereas, the fuel burns for power. It is a simple system that works, but unfortunately, it is not clean; since the separation can't be complete and sludge build-up is much faster than the four-stroke.

In a two-stroke engine, there is no dedicated oil sump or oil pump, yet engine oil is an essential part of the coolant system of an engine. So, the oil is mixed with fuel, and since it is heavier, it gravitates to lubricate the rings so they don't seize from heat and wreck the engine.