Marinate the fish in the oil and lemon juice for at least 30 minutes before grilling. Grill for 10-15 minutes, turning once. The length of time depends upon the thickness of the fillet.
Heat the butter in a saucepan and stew the garlic for about 3 minutes, stirring frequently. Do not let it brown. Ad the basil and a dash of cayenne pepper. Remove the pan from the heat.
Either pour the garlic butter over the top of the fish just before serving, or serve it in a sauceboat on the side.