It is a Lhankhang attached with a resident house of Ap penjor of mombitshokha. It was constructed more then 200 years ago.
It is believed that a Phup once came flying from Bhaay, landed on the Goemhay area but again it did not stay there and flyed over to the place (now lungkha lhakhang) near a cypress tree and stayed there. When the 2nd Gyelwa Karmapa came to visit Haa, he said that the Phup‘s lungthen was in the place and recommended to built a lhakhang in this area.Therefore, the name was also directly derived from the Phup‘s Lungthen and named the Lhakhang as Lungkha.
Source:Ex-Gup Tshewang Penjor(verbally)