UDS:
Never heard the story, but it’s unlikely to be true. A lighthouse on a barren waterless rock would be staffed by single lighthouse keepers, not by anyone with a family and young children. Why would the lighthouse authority want to take on the cost and responsibility of provisioning an infant child on a barren rock? If the lighthouse keeper marries, he’ll be transferred to a more family-friendly station. Or, his family will live on the mainland and not see him that often.
Sounds reasonable, and yet…
http://www.maritimenz.govt.nz/Commercial/Shipping-safety/Aids-to-navigation/Lighthouse-keepers-their-work-and-family-life.asp
I searched through 400+ links looking for it (insomniac for many years now) but no luck. Plenty of crazy lighthouse stories - crazy and homicidal keepers, crazy and depressed wives, crazy and upset ghosts.