It's impossible to prove a negative, so I can't say definitively that there have never been any Jews who lived long-term in Tibet. What I can say, however, is that if a Jewish community existed in Tibet, documentary evidence is slim and obscure at best. We have records of Muslim and Sogdian communities in Tibet, and a lot of documentary evidence for the effects that these communities had in the history of the land and culture, but not so much for any Jewish communities. My pocket dictionary, while not an authoritative historical source, does use the historical terms that I'm aware of for Buddhist, Christian, and Muslim (nang pa, ye shu, and kha che, respectively), but uses an English loan-word for "Jewish," (ji'u). \
The Tibetan term that would correspond to Buddhist (though this is under debate) is "nang pa," literally "insider." There's debate because Bonpos who regard themselves as insiders, but not as followers of the Buddha Shakyamuni, would say that they are nang pa (insiders), but not sangs rgyas pa (followers of the Buddha). To not be nang pa, would mean one would be phyi pa (outsiders). And this is the word reserved for foreigners. To be a nang pa is equivalent to what it means to be Tibetan, and to not be nang pa, even if one's religion has roots older than Tibetan Buddhism, and be labeled a foreigner is clearly problematic. But not really here.
Muslims: Anyway, the other terms are pretty simple. "Ye shu" comes from the word for "Jesus." While "kha che" comes from the Tibetan translation for "Kashmir" which is where (from the Tibetan perspective) Islam was diffused into Tibet. Though the first Khache community was probably seeded into Tibet from Kashmir, later groups of Tibetan Muslims were ethnically and culturally Tibetan, owed political allegiance (largely) to the Dalai Lamas, and lived in Lhasa, while being known especially for their good business practices. The name, however, stuck. The Khache communities took root around 1642 after the Fifth Dalai Lama became the temporal ruler of Tibet and continued to be represented in Lhasa urban and civic life until modern times. Today the Hui community in Lhasa uses a rebuilt mosque that was originally constructed for use by the Khache communities.
The Sogdians: The other avenue to explore, though far far less certain would be the Sogdian community. And I mention him because he is a good historian, though his more recent work is questionable at best. Christopher I. Beckwith wrote a very detailed and important book on The Tibetan Empire in Central Asia. Then more recently he wrote a book called "Empires of the Silk Road" which is much more of a general overview of the central Asian cultural complex and the trends that passed back and forth from one end to the other. Then the last fifty pages went into a really odd diatribe against modernism (it started both Nazism and Communism!) and postmodernism (it doesn't make sense and anything means anything!). But in the middle of the text, Beckwith notices an odd issue regarding timing and essentially proposes that there was a conspiracy in the four major empires of the world in the mid-700s: in Karolingian Frankia, Ummayad Arabia, T'ang China, and Yarlung Tibet, massive, virtually simultaneous revolts took place with the (Beckwith alleges) aim to place compliant, or even ethnically Sogdian and religiously allied, regimes in place. The major results of this campaign were rather obvious: the An Lushan Rebellion in China (An was a common Sogdian surname, and it is used as evidence to prove that An Lushan himself was half Sogdian), and the Abbasid Revolt in the Arab Empire. Two comparatively smaller revolts occurred in Tibet (Sogdians again) and (Beckwith alleges) among the Jewish class in Frankia.
Ok, so before I go any further, I want to say that again, this is entirely theoretical. As far as I know, no one else is proposing a continent-wide conspiracy between merchant classes to overthrow four empires and establish compliant regimes. However, if I was going to research the history of Jewish interests in Tibet, I would start in these two areas.
That said, Beckwith's theory would revolve around the idea of huge, expansive Silk Road businesses. Not a crazy idea in the slightest. We have evidence of Chinese silks winding up on Mediterranean markets, and Parisian silver building fountains in Karakorum. The Sogdians, and this is not theoretical, controlled the Silk Route from Xi'an to Constantinople and were friendly, rivallous, and certainly had their own self-interests. If they were all around Persia, the Middle East, and made it as far as Europe, they would have doubtless come into contact with Jewish and Hebrew speaking and writing peoples. Just by virtue of geographic proximity, but also if we were looking at the economic and commercial behavior and interests of Jewish peoples in those eras. So if there was a Jewish community of any size in Tibet, researching the Sogdians and their interests in Tibet might be an interesting place to start. It would probably be as far back as any reliable records could be trusted (barring a Hebrew manuscript suddenly turning up in a cave in Ngari, Tibetan written language dates back to the 630s, so the Sogdians are about as far back as we can reliably trace documentary evidence of them in Tibet).
And of course, Tibetan Muslims - who have a much more modern history in Tibet, though there was contact between Tibetans and Muslims for centuries before a community of around 50 or so Khache were invited to settle in Lhasa, dating back to this theoretical continental conspiracy, when Tibetans allied with the Arabs to push back the T'ang Dynasty from Central Asia in the Battle of Talas River, itself being a major factor in triggering the An Lushan Rebellion - have been in contact with Jewish peoples for years. Tibetan Muslims, like their Sogdian neighbors, were renown for their commercial skills and were well traveled, often going on pilgrimage to Mecca (through the sea route out of Goa. Being well traveled in this part of the world, and of course learning Arabic and reading the Qur'an (in which there are mentions of Judaic peoples) Tibetans would have come into contact with Jews.
tl;dr: Though it's not evidence of a long (or even short) term Jewish community in Tibet, these are the two leads that I, as a Tibetan scholar, would investigate if I was trying to find evidence of Jewish peoples in Tibet. That said, while it's impossible to prove a negative, as of today, there's no obvious evidence for a long-term Jewish community that had an impact on Tibetan social or economic life.
Sources:
The Tibetan Empire in Central Asia by Christopher I. Beckwith
Empires of the Silk Road by ibid.
Islamic Shangri-la by David G. Atwill