Lughaya is remote even by Somaliland standards. The nearest airport with scheduled flights is Berbera (BBO), about 200 km east, served from Hargeisa, Dubai, and Addis Ababa. Hargeisa airport (HGA) is further inland but has more flights.
From Berbera or Hargeisa to Lughaya is a long drive on poor roads — typically a full day with a 4×4, longer in the wet seasons. Public transport (shared minibuses, qansaaha) runs irregularly; most visitors arrange a private vehicle with a driver who knows the route. The crossing into the Awdal Region passes through several local-administration checkpoints; carry your passport, your Somaliland visa, and a Somaliland-issued security travel permit (the SPU, Special Protection Unit, is mandatory for foreign travel in much of the region — arrange this through your hotel or guide in Hargeisa before setting out).
Travel to Lughaya without a local fixer is not advisable. Conditions on the ground change quickly; consult your embassy's current travel advice.