Prepare the Lobster: Chop the cooked lobster meat into bite-sized pieces and set aside.

Poach the Eggs: Fill a large saucepan with water, add the white vinegar, and bring to a gentle simmer. Crack each egg into a small bowl or ramekin. Carefully slide the eggs, one at a time, into the simmering water. Poach for 3-4 minutes until the whites are set but the yolks are still runny. Remove with a slotted spoon and drain on a paper towel.

Make the Cajun Hollandaise Sauce: Set a heatproof bowl over a pot of simmering water (double boiler). Whisk together the egg yolks, water, and lemon juice. Continue whisking until the mixture thickens. Slowly drizzle in the melted butter, whisking continuously until smooth and creamy. Stir in Cajun seasoning, salt, and pepper.

Assemble the Eggs Benedict: Place toasted English muffins on plates. Top each half with lobster meat and a poached egg.

Drizzle with Cajun Hollandaise: Spoon the hollandaise sauce over the eggs and lobster. Sprinkle additional Cajun seasoning.

Garnish and Serve: Garnish with finely chopped chives and serve immediately.