It's pretty well known that 2-stroke motors usually run on a fuel-oil mixture - in the past, you had to mix it yourself. The only exception I know of is *really big* 2-stroke engines which are occasionally found in locomotives, but these tend to be diesels anyway, and thus fall into a different category.
The *reason* for not having a separate oil sump is that the crankcase is used for the compression phase in a two-stroke engine, and that's where the oil is needed most. Two-stroke diesels operate on a different principle
, and don't have fuel present in the intake air anyway.