Preheat the grill to medium heat (400℉ to 450℉).
To prepare the lobster, use a pair of kitchen shears and cut down the center of the spine (or the top of the tail) lengthwise.
Place the lobster tails and the shrimp in a large bowl. Drizzle with avocado oil and season with salt, pepper, and Old Bay seasoning. Gently toss until coated evenly.
Place the cedar planks on the grill, about 3 minutes. Once hot, place a lobster tail on each plank. Cook, covered, for 5 minutes.
After 5 minutes, push the tails to the edge of the plank, then evenly divide the shrimp amongst both planks. Cover and cook for about 6 minutes, flipping shrimp halfway through, until they are no longer opaque.
Carefully remove the the lobster and shrimp from the grill and serve with the garlic-herb butter. Garnish with fresh parsley and serve.