1. Cut chayote in half lengthwise. Cook chayote in boiling water 3 minutes; drain. Rinse with cold water; drain well. Peel chayote; discard seeds and membranes. Cut chayote into 1/2-inch cubes. Place in a large bowl.
2. Combine 1 cup ice water and onion in a small bowl. Cover and refrigerate.
3. Add bell pepper strips and next 4 ingredients (through hearts of palm) to chayote.
4, Combine juices and next 5 ingredients (through sugar) in a small bowl; stir well with a whisk. Add juice mixture to chayote mixture; toss gently. Cover and refrigerate at least 3 hours.
5. Drain onions well. Place 1 lettuce leaf on each of 6 plates; top each serving with 2/3 cup pepper mixture. Top each serving with onion and 2 teaspoons olives.
Beer note: This salad is soaked in citrus juices, making a German hefe-weizen the perfect choice. Paulaner Hefe-Weizen ($9/six-pack) offers a distinctive banana aroma, while a refreshing tartness from the use of 60 percent wheat helps it to stand up to the high acidity. —Jeffery Lindenmuth