Melt 4 tablespoons of the butter in a small saucepan; when it begins to bubble add the flour. Cook the flour and butter over medium heat, while stirring, for 5 minutes. Stir in the milk and cream. Bring the sauce to a boil, then lower the heat to a low simmer. Stir the sauce thoroughly to remove any lumps. Simmer the sauce for 10 minutes, remove it from the heat, and set it aside.
Split the lobster tails lengthwise, and remove the meat from the shells (do not discard the shells). Dice the meat into large pieces and set it aside, reserving any juices that may accumulate. Heat the remaining 4 tablespoons of butter in a large heavy-bottomed skillet. When the butter begins to bubble add the pieces of diced lobster, the lobster shells, and the minced shallot. Saute these items for 3-4 minutes, taking care not to burn the shallot. Stir in the paprika; saute another minute longer. Remove the skillet from the heat, and very carefully stir in the sherry.
Return the pan to the heat (be careful, the sherry may ignite). Add any juices that may have accumulated on the plate were the diced lobster was resting. Reduce the sherry by half. Stir in the previously made cream sauce. Bring the sauce to a boil, then lower it to a simmer. Simmer the lobster for a minute or two, just until the sauce is thickened and the lobster is cooked throughout. Remove the shells from the sauce and discard them. Serve the Newburg over toast points, rice pilaf, or puff pastry.