Mix flour, salt, pepper and lemon pepper in bowl until well blended. Reserve 4 1/2 tablespoons of seasoned flour in a small bowl and set aside. Rinse fillets and pat dry. Dredge groper in the seasoned flour.
Melt the butter in a frypan over medium-high heat. Place the groper in the frypan and cook until lightly browned and the fish is easily flaked with a fork, 2 to 4 minutes on each side. Remove from frypan and set aside.
Drain any remaining butter in the frypan and wipe clean. Add the chilled butter and lemon juice to the frypan. Cook and stir until the butter is melted. Gradually whisk in the reserved seasoned flour; cook and stir for 5 minutes. Stir in the hot milk, whisking constantly until the sauce has thickened, about 5 minutes more. Serve sauce over the grouper.