Most people prefer Vulcan logic. It's easier when things are black and white.

Logical thinking is based on reasoning from known first principles. All conclusions derived from the same axioms will be the same. This isn't exactly exciting, and doesn't leave much for interpretation or innovation. It's expected to solve problems in a direct, straight-forward way.

Lateral thinking is more interested in pulling in additional context, or destructuring and recombining contexts in order to facilitate new ideas. It deliberately avoids obvious approaches, and therefore, it can be harder to work with.

Of course, Lateral and Logical thinking are not mutually exclusive designations, and the perceptive problem solver will notice we tend to vacillate depending on the situation. Indeed, lateral thinking enables better brainstorming, while logical thinking enables better decision-making.

Diverge for opportunities, converge on solutions

Fewer folks are comfortable with lateral thinking. I assume it's also probable that creative thinkers are more on the lateral tip, while engineers or scientists are more on the logical tip. Know where you are on this spectrum, and where your peers are. Lateral thinking require patience and care when communicating an idea. It's necessary to know if your peers are ready for it.

Because of the dependence on a larger and unexpected context, communicating can be more difficult. Folks are not expecting what you are about to share with them. It's entirely possible that you lose your audience if they aren't ready, eager, and motivated.

If you suspect that your idea is a little fuzzy, it's a good idea to take it back to the shop for another pass before presenting it. A visual aid can go a long way.

Lateral Thinking - How can Lateral Thinking help you?
Lateral Thinking is the step by step process developed by Dr. Edward de Bono, Learn more at his official site.
Lateral thinking - Wikipedia