As it happens I just traveled Lingmethang road, and, as with much of Bhutan, its hard to classify. Which ecozone it is in might not be that helpful, ultimately. At its start, at the village of Lingmethang, it is low elevation (maybe 800 masl?) dry scrub/conifer. Being on the lee side of some serious mountains, it is at the same elevation as Dewathang (where I lived), but it feels like a different planet. Dewathang is very moist warm broadleaved forest.
The road continues all the way to Thrumsingla which is at almost 3800 masl. It has broadleaved forest, coniferous, mixed, near alpine, etc. No grasslands to speak of, no true alpine, and it isn't nearly as wet as the southern foothills, but besides that it runs the range of the country, vegetation-wise.
I'm sure that doesn't help, but thought I'd mention it.