When Is the Best Time
The tourist season on Lampedusa starts at the beginning of June and ends in September. During this time, the island is busy. From my experience, it is best to visit the lighthouse early in the morning or in the evening. During this time, you can have the place just for yourself.
Location and Tips
Faro di Capo Grecale is a lighthouse on the solitary island of Lampedusa. The lighthouse itself was built in 1855 and since then served as a navigation point in local waters. There are beautiful views from the surrounding cliffs. Note that this place can sometimes be very windy.
You can find a short video from the place here on Youtube