Serious, informed answer: A two stroke engine uses ball/roller/needle bearings. They need a thin film of oil, not splash or pressure feed like a four stroke, which uses friction bearings. The piston bottom moving up pulls the next fuel/oil/air charge into the crankcase while compressing the earlier charge above it. It's during this period when the fuel/oil mix is stirring around in the crankcase that some of the oil is deposited on the bearing surfaces.
The point being, proper lubrication of the bearings (and cylinder wall) is accomplished by a fog of dissolved oil. So, proper lubrication can be provided by any mixture which allows a fine fog of oil to be transported with the incoming charge. This is very easy to accomplish with gasoline since the oil is easily dissolved to be carried by the fuel. Oil is nearly insoluble in ethanol, so some other means of injecting a fine mist of oil would be needed. Typical motorcycle oil injection systems count on the gasoline to dissolve and distribute the oil inside the crankcase, so they don't need to aerosolize the oil.
Without knowing what type of engine you are asking about, it isn't possible to suggest modifications to the machinery to create a lube system that would not rely on gasoline to distribute the oil. My guess is you are thinking about something fairly small and inexpensive, which rules out redesign/modification to provide a substitute method for oil delivery.
If your main consideration is cost, I believe they sell gallons of two-stroke oil for motorboat engines. This plus gasoline will be your least expensive fuel.
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