Vertical thinking is digging the same hole deeper.
Lateral thinking is trying again elsewhere. An explanation from Edward de Bono, British physician, psychologist and author. He defines lateral thinking as a technique of problem solving by approaching problems indirectly at diverse angles instead of concentrating on one approach at length.
With logic you start out with certain ingredients just as in playing chess you start out with given pieces. In most real life situations the pieces are not given, we just assume they are there. We assume certain perceptions, certain concepts and certain boundaries.
Lateral thinking is concerned not with playing with the existing pieces but with seeking to change those very pieces. Lateral thinking is concerned with the perception part of thinking. This is where we organize the external world into the pieces we can then process. A person uses lateral thinking to move from one known idea to creating new ideas.