Place beans in large bowl. Add enough cold water to cover by 2 inches. Let beans soak overnight.
Drain beans. Place in heavy large saucepan. Add bay leaves and enough cold water to cover by 2 inches; bring to boil. Reduce heat to medium-low and simmer 30 minutes. Add salt and continue to simmer until beans are tender but still hold shape, about 15 minutes longer.
Drain beans and place in large bowl; discard bay leaves. Add onion and parsley. Whisk oil, lemon juice, cumin, and cayenne in medium bowl. Season dressing with salt and pepper. Pour over bean salad; toss gently to combine. Do ahead Can be made 2 hours ahead. Let stand at room temperature.
Arrange lettuce leaves on individual plates or on large platter. Spoon bean salad into lettuce and serve.