In a medium bowl, combine oil, thyme, lemon zest, and garlic. Add shrimp; toss to coat. Cover and refrigerate at least 4 hours.
In a bowl, whisk together vinegar, mustard, and honey with dry ingredients; add oil in a thin, steady stream, whisking until blended. Cover and refrigerate.
Preheat and oil grill. Cook bell peppers over medium-high heat until charred on all sides, about 10 minutes. Transfer to a plastic storage bag; seal. When cool, remove blistered skin with a small knife. Cut peppers in half; remove seeds; dice into large pieces. Transfer to a large bowl.
Meanwhile, grill tomatoes, corn, onion, squash, and asparagus until evenly charred; transfer vegetables to a large platter. Cut kernels from corncobs; transfer to bowl with bell peppers. Dice remaining grilled vegetables into large pieces; transfer to bowl with bell peppers. Add avocado and salt. Set aside.
Remove chicken from marinade, leaving as little marinade on chicken as possible. Season with salt and pepper. Place chicken skin side down on grill over medium-high heat and cook about 8 minutes. Turn and grill until chicken skin loses its pink color throughout, 6 to 8 minutes. Cool; dice into large pieces.
Remove shrimp from marinade, leaving as little marinade on the shrimp as possible. Season with salt and pepper. Grill 2 minutes per side until opaque.
In a large bowl, toss greens with vinaigrette until evenly coated. Divide among 12 serving plates. Arrange an equal amount of chicken and grilled vegetables on each plate. Garnish with lobster and shrimp.