in most larger oil injected 2 cycle engines the oil metering is proportionally connected to the throttle . as the throttle opens the oil delivery increases and vise-verse. if you are using this oil as a lube for valve train protection, you might be able to set up some linkage to work the same way off the throttle servo. as a throttle servo is very under labored...... there should be plenty of reserve servo power available to easily run another system. proportioning can be achieved through slave levers and/or belcrank(s) to increase, decrease, or reverse pushrod travel to the oil metering valve in proportion to the throttle rod travel.
as far a pump goes. the oil tank could be pressurized by a tap in the crankcase of the engine, using secondary compression or off the silencer, as fuel tanks are pressurized, to pressurize the oil tank, rather than using an electric pump.