This isn't quite "early," but the first Christian Missionaries from the West reached Tibet in the 17th Century. A Jesuit named Antonio D'Andrade reached the western region of Guge (which was at the time affiliated with Ladakh, though it would soon be conquered by the central government of Lhasa) and established a small mission with reportedly some minor success. Thereafter, in 1630, two more Jesuits reached Shigatse, though the death of one caused the mission to abort before anything came of it. The Vatican sanctioned a Capuchin mission that lasted from 1706 to 1711, closing from lack of funds. In 1716, the Jesuit Ippolito Desideri reached Lhasa. Desideri deserves special note, because unlike all other missionaries before and most since, he devoted himself to learning the language and religious beliefs of the Tibetans. In that way, he was able to communicate with them beyond mere formalities and was reportedly well-regarded by the Lhasa elites, though he had little success in converting anyone. He was arguably the first Western scholar on Tibet, with his "Account of Tibet," and his success in openly practicing Catholicism and interacting with the religious and lay figures of Tibet is in no small part attributable to his dedication to studying the Tibetans in a respectful manner. It also helps that he fell in with a Qosot (a branch of the Mongols) princess on his journey to Lhasa and was therefore received quite favorably. However, within several decades all Jesuit and Capuchin missions were closed. The Capuchins seem to have made little attempt to learn Tibetan language or customs, instead contenting themselves with knowledge of a few evangelical slogans. They were politely received, it seems, but little more. It wasn't until 1741 that any Tibetan converts were made, and the result was disastrous. One of the Tibetan converts was tasked with delivering gifts to the Dalai Lama. This convert, Tomaso (his Christian name, a Latinization of Tenzin) refused to prostrate himself before the Dalai Lama, and thereafter arguments broke out regarding the Christian view that the Dalai Lama was not reincarnated and Sakyamuni was not a true saint. The missionaries were then shunned and ostracized for several months, before being sternly upbraided for their perceived disrespect. From the Tibetan perspective, they had been extended every courtesy and hospitality, and now were teaching Tibetans to insult their rulers and religion. The missions remained for several more years, but little came of them after the lamas and nobility turned their backs on them, and they closed around 1750.

It should be noted there were other missionaries at the time besides those I've mentioned, but not a great number. As far as their perceptions of each other (the Tibetans and the Catholics), the Tibetans seem to have regarded them with curiosity and tolerance, though little real interest in their mission or values. Tibet was not "closed" to outsiders at this time, but for most of its history as a Buddhist nation, Tibet has had little interest in the offerings of outside cultures not directly connected to their religion.

The various missionaries, in turn, seemed to have little idea what to make of the country. With the exception of Desideri and some others, few of them knew much about Tibet or the people they interacted with. In fact, some early missionaries arriving in Tibet are reported to have believed they found some odd branch of Christianity, with pictures of the Tibetan goddess Tara confused with that of the Christian mother of Jesus, Mary. Later, when British expansion in India brought Protestant missionaries to Tibet, some of these missionaries apparently disfavored the analogies with Catholicism they saw in Tibetan Buddhism.

It is also quite likely that, centuries before this, Tibetan Lamas had contact with Nestorian Christians at the court of the Mongol Khan. However, I am unaware of any writings by one side regarding the other (though they could certainly exist).

Source: David Snellgrove and Hugh Richardson, "A Cultural History of Tibet." 1967.

Kuchlug was a 13th century leader of a Mongol tribe known as the Naimans. Kuchlug was a Nestorian Christian, like his tribesmen. He was defeated and driven West by Genghis Khan to the Kara-Kihtan Empire where he sought and gained refuge. He married one of the ruler's daughters and converted to Buddhism (his new wife's religion). He then rebelled against and overthrew his father-in-law.

Once in power, Kuchlug set about suppressing Islam in his territory, while being tolerant/supportive of both Christianity and Buddhism. Perhaps this area of interaction between Eastern Christianity and Buddhism, is the kind of thing you are looking for. Unfortunately, I don't have more to add about the inter-religion relations that this historical narrative implies must have happened. I do believe that, while the majority of the population of the Empire were Muslim, but there were both Buddhist and Nestorian minorities.

Kuchlug's religious persecution of Muslims undermined his own power and alienated much of his realm, which invited Ghengis Khan to work him over again (for good this time).