Place shrimp in a medium bowl. Mix with half of the ginger dressing. Cover and refrigerate for 20 minutes.
Thread shrimp onto pre-soaked wooden skewers.
Pre-heat a grill or grill pan to high heat. Grill shrimp until cooked through, 2-3 minutes per side. Remove from heat. Using a fork or tongs, slide shrimp off of skewers and place shrimp in a bowl covered with foil to keep the shrimp warm.
In a medium bowl, toss together pineapple, mango and papaya.
Divide lettuce equally among salad plates and top each plate with even amounts of pineapple mixture, avocado slices and shrimp. Drizzle with reserved dressing.
Place garlic, ginger, cilantro, lemon zest and juice, and oil in a food processor. Blend until smooth.
The grilled shrimp can be served warm or cold with this salad.