> Further than Zen? Which branch are you considering orthodox? And how are you measuring distance from it?
Distance in terms of belief and time. The most 'orthodox' and also the oldest extant sect is Theravada Buddhism (mainly centred around Sri Lanka, Myanmar, Thailand, but also with historic temples in India and elsewhere), although there is also the argument that some of the older Mahayana sects may have some succession to the Mahasamghika, but strictly speaking the oldest references to the 'Mahayana' are from the 1st century BCE, and the Theravada can be traced to the 3rd century BCE.
Anyhow, Tibetan Buddhism came as a result of various influences, including Indian Tantric Buddhist missionaries (Tantric beliefs, which originate in Saivism, a cult within Hinduism, appeared in Buddhist texts from the 3rd century CE onward, and of course don't appear in early Buddhist texts), the native Bon religion (animistic and shamanistic), and then-current Mahayana Buddhism. The origins of Tibetan Buddhism are fairly well documented, with Buddhism reaching Tibet in the 7th century CE, and it being adopted as the state religion in the 8th century CE.
> Who in Buddhism would you count as a peer, or someone more important than the Dalai Lama, in the present day?
Buddhism isn't supposed to have a central leader. It's supposed to be centred on the teachings of the Buddha, although there are prominent monks with fairly wide influence in all the major schools.
It's kind of like in Christianity. Prior to the great schism, you had the unified Orthodox/Catholic church which had 5 Patriarchs (Rome, Constantinople, Antioch, Jerusalem, Alexandria). Rome split and became huge and monolithic, the Orthodox were less centralised so when they spread, they established more 'Patriarchates' with more or less equal importance to the historic ones; in addition to the Patriarchs of Constantinople (New Rome), Alexandria, Antioch and Jerusalem, you also have Patriarchs of Moscow (3rd Rome), Georgia, Serbia, Romania and Bulgaria, in addition to Archbishops and so on. So even though Orthodox Christianity is nearly as widespread as Catholicism (arguably more widespread in the 'old world'), they don't have a visible 'leader' because of the flat power structure.
Tibetan Buddhism adopted a more vertical power structure because the Dalai Lama's sect eventually achieved political power over Tibet, whereas other schools of Buddhism maintained the flat power structure that existed in early Buddhism.
> Whatever the reason he became famous for, he's probably done probably the single most influential figure to influence the West's familiarity and understanding of Buddhism.
Familiarity yes, but not understanding. There have been many other Buddhist teachers who have actually brought the religion to the west (not only from Theravada, Mahayana, Ch'an, Zen and Vajrayana schools, but also from different sects of Tibetan Buddhism). Tibetan Buddhism contains some tantric beliefs which most westerners wouldn't even recognize as Buddhist, for example, consort practice https://en.wikipedia.org/wiki/Karmamudr%C4%81.
Edit - should also add, Tibetan Buddhism/Vajranaya has the fewest adherents of the major schools, making it the least important Buddhist school as far as demographics go. Mahayana Buddhism (Zen/Ch'an, Pure Land, and other smaller Mahayana sects/regional variations) has the highest number of adherents, although is fragmented and many adherents may also follow other religions like Taoism and Shintoism. Theravada is probably the largest school with the most consistent teachings across its regional variations (150 million adherents). By contrast, there's 3 million people in Tibet, perhaps 10 million people worldwide who nominally belong to a Vajrayana Buddhist sect (including Tibetan exiles)...