Pound the conch meat with a mallet until tender. Chop into bite-size pieces. Place in a bowl, sprinkle with lemon juice, and set aside.
Heat the oil in a skillet over medium heat, and cook the garlic, onion, green bell pepper, red bell pepper, celery, and mushrooms until tender. Mix in the tomatoes, Worcestershire sauce, ketchup, and sugar. Season with red pepper, salt, and pepper. Bring to a boil. Reduce heat to low, and simmer uncovered 20 minutes, stirring occasionally.
Mix the conch meat into the skillet, and continue to cook 10 minutes. Do not overcook, or the conch will become tough.