Whisk together first 7 ingredients in a bowl until well blended. Set aside.
Cook potatoes in boiling water in a large saucepan 10 minutes or until tender; drain. Toss warm potatoes, green onion, and 1/2 cup of lime marinade in a bowl until vegetables are coated. Marinate, covered, 2 hours, stirring occasionally.
Place shrimp into boiling water in a saucepan. Remove from heat. Let stand, covered, 3 to 5 minutes or until shrimp turn pink; drain. Peel and devein shrimp. Toss shrimp with 1/4 cup of marinade in a bowl. Marinate, covered, in refrigerator 2 hours, stirring occasionally.
Line a serving platter with lettuce leaves, and mound potato mixture in center. Dip avocado slices into remaining marinade. Arrange avocado slices, shrimp, tomatoes, and watercress around potatoes, and drizzle with remaining marinade.