Place potatoes in a large pot of salted cold water. Bring to a boil and cook until just cooked through, about 10 to 12 minutes, but varies based on size of potatoes. Drain, let cool slightly, and cut into 1/2-inch dice. Combine the potatoes and lobster in a large bowl.
Whisk together the mayonnaise, mustard, horseradish, vinegar, and garlic in a medium bowl and season with salt and pepper. Add the mayonnaise mixture to the potato-lobster mixture and stir gently until combined. Fold in the scallions and tarragon and re-season with salt and pepper, to taste. Serve immediately.