Can you really use old motor oil to fertilize a lawn? If yes, is there some special way to do it/mix it?
No, but your lawn fertilizer could, after millions of years, be refined into motor oil. 
Good God, no. And for the second part of your question, yes, but not for your lawn. Read on here.
Back before the EPA existed, my father used to edge the yard with old motor oil. It kills grass, and I don’t think it has much nitrogen in it. I don’t see how you could use it as a fertilizer.
This guy at a group I go to seems to think you can. But I can’t talk about it. That’s the first rule. And the second rule is that I’m not supposed to talk about it.
If you do that your grass is gonna be brown for several years. At least mine was.
There’s a joke about Australians watering their gardens with motor oil, but it’s not meant to help the plants grow. Its meant to preserve the, er, buried treasure, shall we say? 
C’mon Lou, let us use your basement!