Heat oil in a saucepan over medium heat until hot. Sauté mamey, onion, and garlic 5 minutes. Add water, wine, and bay leaf; bring to a boil. Reduce heat and simmer, uncovered, 10 minutes or until tender. Remove and discard bay leaf.
Pour mixture into a food processor or blender, cover, and process until smooth. Pour through a wire-mesh strainer into a bowl; stir in lime juice and salt.