From Solomon Islands Broadcasting Corp.
Minister Folatalu told Parliament, Lomlom Airport has been completed and is proposed to be officially opened in January 2014.
In June 2013 from the Solomon Star:
New airport: Lomlom, in Temotu province, one of the Reef Islands.
solomonstarnews.com/news/national/18109-pm-to-open-new-airports
See also (translate from Italian):
http://it.wikipedia.org/wiki/Lomlom
Still no sign yet of FlySolomons flights to there.