In a medium saucepan cook chayotes, covered, in a small amount of boiling salted water for 5 to 6 minutes or until tender; drain. Rinse with cold water to stop cooking; drain well. Transfer to a medium mixing bowl; add garbanzo beans.
For marinade, in a screw-top jar combine lemon juice, olive oil or salad oil, water, basil, sugar, salt, and garlic. Cover and shake well. Pour marinade over chayote mixture, stirring to coat well. Cover and marinate in the refrigerator for 3 to 24 hours, stirring occasionally.
To serve, drain chayote mixture, reserving marinade. Stir in olives. Spoon chayote mixture onto 6 lettuce-lined plates. Top each serving with chopped red onion and tomato wedges. Drizzle with some of the reserved marinade. Makes 6 side-dish servings.