Is there a vegetarian diet in order to lose 20 pounds in about 2 or 3 months for a 14 year old girl?

Be VERY careful: Whether this is her idea or your strong urging, vegetarianism must be an individual's informed choice. It is dangerous unless the person knows exactly what she is doing and supplements accordingly. No weight loss plan, especially in a minor, should be undertaken without a physician's very close supervision. And as a parent -- consider starting a family fitness program instead with you as leader.