The records are at NAS in Edinburgh.
Northern Lighthouse Board's website is at
nlb.org.uk
The relevant info:
If you want to carry out research on the Northern Lighthouse Board or are trying to trace your family tree and think you have lighthouse connections, you will need to know how to access to the Boards Archival Records.
The Northern Lighthouse Board's archive records are now on deposit at The NATIONAL ARCHIVES of SCOTLAND. They have a comprehensive website, which can be visited on http://www.nas.gov.uk or you can contact them at HM General Register House, Edinburgh, EH1 3YY Tel: 0131 535 1314 Fax 0131 535 1360.