With vertical thinking one may look for different approaches until one finds a promising one. With lateral thinking one goes on generating as many approaches as one can even after one has found a promising one. With vertical thinking one is trying to select the best approach but with lateral thinking one is generating different approaches for the sake of generating them.
I have often asked myself if I would have worked as hard if I was as ill as Steve Jobs. My answer is that my wife most likely would not have let me work, and I would have stayed home. But I am not Steve Jobs.