There have been a few songs about lighthouses but probably none about lighthouse keepers' wives, or aspiring wives of same. As the last UK lighthouse was automated in 1998, the lady who wrote this song will have to continue to aspire.
The lady concerned is Erika Eigen, who was a member of the short lived psychedelic folk band Sunforest. Little is known about her, but on August 6, 2008 she turned up in Battersea, South London, where she performed it ad hoc with American guitarist Fred Sokolow.
"I Want To Marry A Lighthouse Keeper" or simply "Lighthouse Keeper" was used in the 1971 film A Clockwork Orange.
Suggestion credit: Alexander Baron - London, England, for above 2