Ensure lobster and crab meat are fully cooked, cooled, and free of shells or cartilage. Pat the meats dry with paper towels to remove excess moisture. Chop lobster into 1/2-inch pieces and flake the crab meat into bite-sized pieces. Place in a mixing bowl and toss with lemon juice and 1 teaspoon Old Bay seasoning; set aside for 5 minutes to allow flavors to marry.

Make the Base

Soften and Combine

Preheat oven to 375°F (190°C). In a medium bowl, using a hand mixer or sturdy whisk, beat the softened cream cheese until smooth. Add sour cream, mayonnaise, Dijon mustard, Worcestershire sauce, minced garlic, and minced shallot. Beat until fully combined and glossy, scraping the bowl sides.

Add Cheeses and Seasoning

Fold in grated cheddar and grated Parmesan until evenly distributed. Season the mixture with salt and black pepper, adjusting to taste. Stir in chopped parsley and optional hot sauce if using.

Combine Seafood and Base

Gently fold the prepared lobster and crab mixture into the cheese-and-dairy base, taking care not to break up the chunks of seafood. Taste and adjust seasoning with an additional pinch of salt, pepper, or Old Bay if desired.

Bake and Finish

Transfer the dip to a 1-quart oven-safe baking dish (or a shallow pie dish). Smooth the top with a spatula. Mix the melted butter with smoked paprika and brush lightly over the surface of the dip or sprinkle paprika and dot with small bits of butter for a golden finish.

Bake in the preheated oven for 20–25 minutes, until the edges are bubbly and the top is lightly golden. If you want a more browned top, place under the broiler for 1–2 minutes—watch carefully to avoid burning.

Remove from oven and let rest 5 minutes. Garnish with additional chopped parsley and a light sprinkle of Old Bay if desired.

Serve

Serve warm with toasted baguette slices or crackers and lemon wedges on the side. Squeeze a little lemon over each portion if desired.