There's a lot of assumptions to unpack there, so I'm going to try to be as brief as possible while also answering the question.

someone whose claim to fame is living in exile from his homeland where he claims the right to be a theocratic monarch. Generally, when it's closer to home, we tend not to be very fond of those. The other example of a similarly treated character I can think of is Ruhollah Khomeini, who received a lot of exposure in France in the 70's.

This comparison seems pretty off to me, though I don't know much about contemporary Persia so I won't try to parse it apart. What people tend to forget is that Tenzin Gyatso, the current Dalai Lama, was enthroned when he was four years old. His country was invaded when he was fifteen. He became the political monarch of Tibet at sixteen. And then he ran for his life into exile from his homeland at twenty-four. (And it's worth noting that he was completing what amounts to a PhD. in Buddhist Philosophy while trying to balance the powder keg of Tibetan anger vs. the pressure of Chinese authority).

The Ayatollah, on the other hand, was 62 when he was sent into exile and was there for 14 years. Other than the fact that the situations in Tibet and Persia are worlds apart, I think it's worth remembering that the personal experiences and characteristics of the Dalai Lama were, are, and have been capable of changing and shifting, and we can track that over time through documentation.

And he has often been very up front about that. In 2011 he made the decision to step down from any position of political power, transferring the Central Tibetan Authority (the Tibetan government in-Exile) saying, "Religious and political institutions should be separate but while I was saying this, I combined the two myself until now... So in a way it was being a hypocrite."

And yet with the Iranian Revolution fresh in memory, the 14th Dalai Lama was (or remained? I'm assuming he already had some prominence) lionized as an intellectual and embodiment of wisdom.

I... don't know what kind of prominence the Dalai Lama had prior to 1989 or 1979. I don't think it was very much outside of Asia. In the early 2000s I had Bhutanese friends get held up at airports because customs agents had to check maps to make sure Bhutan was a real country, and people still ask me exactly what the difference is between Nepal, Tibet, and Bhutan. I struggle to imagine 1980 as a much different world.

Anecdotes aside, after the Dalai Lama left Tibet in 1959, the CIA continued to provide money and weaponry to groups inside of Tibet. That money and influence stopped abruptly in 1972 when Nixon reached out and tried to form a quasi-alliance with China, which of course meant stopping the funding of China's greatest domestic territorial challenge.

The Dalai Lama was, this whole time, kind of a pain in the neck for the United States politically. In 1950, a US agent counselled the Dalai Lama to leave Tibet for India, Ceylon, or Thailand (in that order) to lead the resistance against the PRC. If he did, the United States could claim plausible deniability over Chinese rule in Tibet, but if he didn't and he chose to work with the Chinese, he would effectively be forfitting Tibetan independence. He chose the latter option rather than plunge his nation into War. It ended poorly less than a decade later, when he repudiated the Seventeenpoint Agreement from exile in India, but the diplomatic damage had been nearly total on Tibet.

It's pretty well known that Communism in general is an Atheistic philosophy. The Soviet Union decimated their churches and the Buryat monk Dorjiev warned the Thirteenth Dalai Lama against the Soviet Union after years of lobbying for Russia, only later to die in a Gulag. The Thirteenth Dalai Lama prophesied on his death bed that the enemies of the Dharma (i.e. Communists) would soon come to destroy religion. Most likely from China.

In this, the United States found common ground with the Tibetan cause, and it boosted the relationship, at least a little bit before setting the stage for 1989.

How did this happen?

The big year was 1989. Recall that by 1972, the United States had given up physical resistance to China via Tibet. Well by 1989 the tide seemed to be turning against the Soviet Union and there were concerns that China might follow in her big sister's footsteps and break apart at the seams. Tibet would be the most likely candidate to chip off first, but then the Tiananmen Square protests happened and were widely televised. The Dalai Lama was awarded the Nobel Peace Prize that year as he continued to preach non-violence in his resistance against China, a decision he had made since 1959. (Arguably earlier, but he had afterward rejected direct assistance for military resistance from the CIA, leading them to try and find closer sources to the conflict area, i.e. within Tibet.)

The Fourteenth Dalai Lama was awarded the Nobel Peace Prize partly as an encouragement of the global anti-Communist resistance, the Dalai Lama symbolizing minority, downtroddened peoples, as well as the symbol of non-violent resistance against those powers. Since China was a nuclear power, any direct confrontation could be catastrophic.

The Dalai Lama's religious role, also made him a symbol of religion prevaling over "godless Communism," at least, that's my own cynical analysis for one reason he was so heavily promoted. At least at first.

Cont'd.