I had a bit of an idea I might try to cobble up at some point in time. You could use an electric pump with a valve, controlled by the throttle. When the throttle is open, oil goes to the motor. However, you will have to somehow determine how much gas is used per minute when running wide open and when idling to find out how much oil is needed. Then this pump would have to be tweaked until it is perfect (which can be done by using various diameter tubes)
However, you will have to be 100% sure that your battery is completely charged, and again, that issue with the tank comes into play, which I don't really thing is going to be a big deal, it doesn't have to be that big. I have a 1 gallon tank on mine and use roughly 100mL of oil, which I find runs pretty good.