Preheat the grill to medium-high heat.
For the Habanero Butter: Combine the butter, garlic, habanero, shallot and capers in a small saucepan over medium heat. Season with salt and pepper and cook until the shallots start to turn translucent. Deglaze the pan with the white wine, lime juice and zest, cook the mixture until the white wine has reduced and the pan is almost dry. Transfer to a small bowl and reserve to the side.
For the garlic butter: Combine the butter and garlic in a medium saucepan and cook over medium heat until the garlic becomes fragrant and softened, 5 to 6 minutes. Add the parsley and mix well. Transfer to a small bowl and reserve to the side.
For the cilantro-lime mayonnaise: Add the mayonnaise, buttermilk, cilantro and lime zest and juice to a large bowl. Season with salt and pepper and whisk to combine. Add the cabbage and mix well to coat. Refrigerate until serving.
For the Southwest lobster roll: Prepare a grill to medium-high heat. Brush the lobster tail pieces with the habanero butter. Place the tails shell-side down on the grill. Cook for 3 minutes, flip the lobster over, baste liberally with more habanero butter and allow the tails to cook in the butter and their own juices until the tails are curled and the meat is opaque, 4 to 6 minutes more. Remove from the grill and reserve to the side.
Brush the hot dog buns with the garlic butter. Grill until golden and crisp, about 30 seconds.
To assemble the southwest lobster roll: Place the avocado slices in the buns. Remove the lobster tails from the shells. Place 2 pieces of lobster tail in each bun. Top with 2 slices of the tomato, followed by 1/4 of the cabbage mixture. Place the Southwest lobster rolls on a large platter and serve immediately.