Since you are close to the lighthouse, you may be able to experiment a little. Try treating it the same as getting an image of the full moon; say f11, pick your favorite ISO and set the shutter speed to 1/ ISO. Then take a longer exposure to get the background and blend the images. Use that as a baseline to speed up the shutter speed until you get what you want.
If you set the aperture to f16 or more with a longer exposure, you could end up getting the star rays, one ray per aperture blade, so be careful about that. Also, show us how they turn out!