To make the Pernod sauce, place 125ml (4fl oz) water in a small pan with the star anise and bring to the boil. Reduce the heat to low and simmer for 10 minutes, or until reduced to about 2tablespoons. Stir in half the Pernod. Whisking constantly, gradually add the butter, a few pieces at a time. Season with salt and ground white pepper, then place the pan in a bowl or pan of hot water to keep warm. (The sauce will separate if placed back over direct heat.)
Add the lobster tails to a large pot of boiling water and cook for 2 minutes, or until the shells turn bright orange. Drain and refresh in cold water.
Place the lobster tails on a cutting board with the soft undershells facing down. Using a large knife, but without cutting all the way through, split the tails in half lengthways down the back, then open them up.
Preheat the grill to high. Brush the lobster flesh with the melted butter, season lightly, then grill, cut-side-down, for 5 minutes. Turn and grill the other side for 5–10 minutes, or until the flesh is firm. Transfer to serving plates. Stir the remaining Pernod into the sauce, then spoon a little sauce over the tail and serve the remainder on the side.