Lungchuzekha goenpa is around 7 km return, 470 m up, 3-4 hrs and if you add Trashigang goenpa and Hontsho then the distance will abe around 10 km/ 550 m up, 4-5 hrs).
Get dropped of at the large chorten in the middle of Dochula. Walk to the far end of pass, just south of the mani wall and chorten. Find the trail that goes uphill. If you cannot find it, head up the ridge, following some of the cattle/horse/
yak trails until you find a recognisable Homo sapiens trail. Follow it up the ridge, then down and up again through a forest of hemlock, birch and rhododendrons. The trail follows the north side of the ridge and then heads back to the ridge into a small meadow
with some junipers. After crossing or joining the ridge a few more times, it passes to the left of a knoll on a stretch of trail that can be very muddy. Next it enters a large meadow, where yak herders camp in winter. When returning, head for the lower side of this meadow.
Go to the end of the meadow, on your left. Here the trail continues on the right side of the ridge through a moss-covered red rhododendron forest with some gigantic hemlocks, junipers that may look like cypresses, and bamboo undergrowth. The trail continues
up. Occasionally, some smaller trails head up to the ridge and rejoin later. Eventually it passes a yak fence and crosses a main ridge. Here it turns left, while going slowly down the other side of the ridge. Soon, the trail joins a larger one coming from Trashigang
goenpa. About 100 m further, a smaller trail goes up to the left to Lungchuzekha goenpa, surrounded by prayer flags, a barbed wire fence, heavily logged slopes, some friendly monks, a cookie-begging cat, and an unfriendly barking dog, which becomes very friendly once you start feeding it your lunch.
On clear days the views from the goenpa are fantastic; after Talakha Peak probably the best in the Thimphu area. All major mountains of Bhutan can be seen: to left the summits of Jhomolhari (7,314 m), Kang Bum (6,500 m), and Gangchhenta (Great Tiger Mountain, 6,840m; the shape of a tiger) appear above nearer mountains. Straight ahead, Masang Gang (7,165 m; the peak shaped like a trident) towers over Gasa Dzong (2,700m), a tiny white speck in a sea of green. Further to the right are the high peaks of Lunana: Tsenda Kang (7,100 m), Teri Kang (7,300 m), Jejekangphu Gang (7,300 m), Kangphu Gang (7,212 m), and Zongphu Gang (Table Mountain, 7,100 m; the very long flat mountain). Further to the northeast Gangkar Puensum, Bhutan’s highest mountain and the highest unclimbed mountain in the world (7,541 m), dominates the skyline. Behind
these mountains lie the plains of Tibet. The Black Mountains stretch along the easternhorizon. To the south lies Hinglay La, while the Dagala range fills the view to the southwest.
From here you can return to Dochula or continue to Trashigang goenpa and Hontsho.
The description of the route is obtained from Mild-mad-hikes from Thimphu.