Perhaps as early as boyhood, the Dalai Lama respected Fascists:

He catered the elect audience saying he saw Nuremberg already on photographs when he was still a child. “Very attractive” with “generals and weapons” and with “Adolf Hitler and Hermann Goering”.

Some of the auditors seemed to be embarrassed, some were “alienated for a second”. Nuremberg’s chief mayor Ulrich Maly calls it a “moment of shock”. The special guests tried to get himself out of the affair by stating that as a child he wasn’t able to foresee the Nazi catastrophe.

(Source.)

During his adulthood, the Dalai Lama would develop good relations with neofascists such as Miguel Serrano and Jorg Haider.

As for Tibet itself, from what I read, the director of the Third Reich’s expedition to Tibet, Ernst Schäfer, received a letter from the Tibetan court stating:

“…His Highness Herr Hitler, King of the Germans, may he be blessed with physical well-being, with serene peace, and good deeds…Greetings from a Divine Ruler to the Fuhrer.”

Elsewhere Ernst Schäfer commented on Tibet’s theocracy saying:

“They are ahead of all the rulers on this Earth, in that they are real kings, absolute leaders, often violent, but usually just. Their way of life is proud and manly.”

I cannot confirm these quotes’ authenticity, but I would be unsurprised if somebody independently verified them.

Five years before German Fascists reached Tibet, the parafascist scholar, Giuseppe Tucci, expedited there. Quoting Elisabetta Porcu’s Pure Land Buddhism in Modern Japanese Culture, pages 42–3:

With respect to Tucci’s involvement in fascism, the programme of his first expedition to Western Tibet in 1933 was accepted, for example, as Tucci himself wrote in the “Preface” to the Cronaca della Missione Scientifica Tucci nel Tibet Occidentale (in English, Secrets of Tibet), “Through the enlightened intervention of the Head of Government” (Benito Mussolini) and the financial support of Italian industry and commerce, among which, of course, were fascist institutions.

Moreover, Tucci expressed gratitude once again to Mussolini at the end of the preface, when, wishing for a second expedition to complete his studies on Western Tibet, he stated that he would have been able to do it only if “the interest of the Head of the Government who [had] made possible [his] expedition, the effective support of the Royal Academy of Italy and the consent of the English authorities in India” had continued to sustain him.

He had some positive things to say about Tibet. Quoting Per Kvaerne in Imagining Tibet: Perceptions, Projections, and Fantasies, pages 55–56:

he expressed a king of admiration for Tibetan society, which he regarded—when he last visited Tibet in 1948—as still uncontaminated by the ills besetting the modern world, chief among which were “politics.” Tucci now claimed that:

The Tibetans are not far different from us: only they were long ensnared by a religious and magic outlook on life, in which the boundaries between the realms of reality and possibility, of truth and imagination, were not clear‐cut ones. The intellect in them had not yet reached such a degree of freedom as to stamp out the dreams of the soul.

The Empire of Japan’s interest in Tibet was relatively minor, but relations between the two antisocialist régimes were apparently friendly overall. Quoting Paul Hyer in Imperial Japan and National Identities in Asia, 1895–1945, page 83:

Aoki had lobbied officials to give greater importance to establishing relations with Tibet stressing the various past contacts that had been made. Among other contacts he cited the visit to Japan in 1939 of a party of ‘living Buddhas’ as representatives of various important temples of Mongolia and Tibet and their laudatory reports about Japan after returning home.

Sadly, I have to confess that the theocracy‐in‐exile’s ties to Fascists and Imperialists is not even among the worst of its problems.