Why did the Zionist terror group Lehi propose an alliance with Nazi Germany and Fascist Italy during WW2 ?

In 1941, Yitzhak Shamir (later on, 7th prime minister of Israel) committed "an unforgivable crime from the moral point of view: he preached an alliance with Hitler, with Nazi Germany, against Great Britain." While still considering themselves part of the Irgun, the Sternists sent a proposal of alliance to the Nazis. "The establishment of the historical Jewish state on a national and totalitarian basis, and bound by a treaty with the German Reich," the Stern document read, "offers to actively take part in the war on Germany’s side." It adds that "the NMO [Irgun] is closely related to the totalitarian movements of Europe in its ideology and structure".
Stern Gang asking Nazi Germany for alliance between both groups.
Source: “The Stern Gang: Ideology, Politics, and Terror 1940-1949” by Joseph Heller who is a professor in the Hebrew University in Jerusalem.
Yitzhak Yzernitsky — later to call himself Yitzhak Shamir, one of the longest serving Prime Minister of Israel, became the operations commander of the Stern Gang after Avraham Stern was killed by the British army in February of 1942. Under Shamir’s leadership, 14 assassinations were attempted on British officials with two successful ones, of Lord Moyne, the British Minister Resident in the Middle East, sitting in Cairo, and the UN Representative to Palestine, Count Folke Bernadotte, who received three bullets in the heart on the order of Stern’s operations commander Yitzhak Shamir.
Count Folke Bernadotte recognised universal human rights and advocated for the Palestinian right of return to their lands and properties they were dispossessed and ethnically cleansed from by the Zionists at that time.
In early 1948, Jewish paramilitary forces began to seize more land in Palestine. By the end of July, more than 400,000 Palestinians had been forced to flee their homes, and their plight as refugees had just begun.
In May of that year, Swedish diplomat Count Folke Bernadotte had been appointed as the UN Mediator in Palestine. His mission was to seek a peaceful settlement. The Count surveyed devastated Palestinian villages and visited refugee camps in both Palestine and Jordan. The scale of the humanitarian disaster became apparent, as he witnessed cramp living conditions, long queues for basic food and scarce medical aid.
Count Bernadotte was no stranger to human disaster; with the Red Cross he had rescued over 30,000 prisoners of war from Nazi concentration camps. Now he advocated the Palestinian's right to return to their homes.
In the first Progress Report dated 16 September 1948 submitted by the UN-appointed Mediator for Palestine, Count Folke Bernadotte, the Mediator recognized the right of return as key to a resolution of the conflict in Palestine. Bernadotte wrote:

"No settlement can be just and complete if recognition is not accorded to the right of the Arab refugee to return to the homes from which he has been dislodged. It would be an offense against the principles of elemental justice if these innocent victims of the conflict were denied the Right to Return to their homes while Jewish immigrants flow into Palestine, and, indeed, at least offer the threat of permanent replacement of the Arab refugees who have been rooted in the land for centuries."

The Count's first proposal argued for fixed boundaries through negotiation, an economic union between both states, and the return of Palestinian refugees - the proposal was turned down.
On 17 September, the day following his UN report, Count Bernadotte's motorcade was ambushed in Jerusalem. He was shot and liquidated by terrorists of the Jewish Stern gang.
The killing was approved by the three-man 'center' of Lehi: Yitzhak Yezernitsky (the future Prime Minister of Israel Yitzhak Shamir), Nathan Friedmann (also called Natan Yellin-Mor) and Yisrael Eldad (also known as Scheib).
Menachem Begin, founder of Likud, the sixth Prime Minister of Israel and a leader of the Zionist terrorist group Irgun, honored Stern by putting his portrait on a postage stamp.
The Charter of the Stern Gang, or more accurately, the principles promulgated by Stern, included the establishment of a Jewish state "from the Nile to the Euphrates", the ‘transfer of the Palestinian Arabs to regions outside of the Jewish state, and the building of the Third Temple in Jerusalem. It maintained offices outside of the Middle East – including Warsaw, Paris, London, and New York City, the latter headed by Benzion Netanyahu, Benjamin Netanyahu’s father.
Stern is still revered today in Israel, and has a settlement named in his honor, as well as a postage stamp.
When Yitzhak Shamir, Israel’s future Prime Minister in the 1980s, was asked to explain their collaboration with the Fascists, he replied:

”The enemy of my enemy is my friend.“ (Tom Segev, One Palestine Complete , p.464).

Jabotinsky collaborated with the Italian fascist Benito Mussolini and both supported each others ideologies. In the matter of fact, an entire Naval Academy in fascist Italy was established to train Zionist militias. This was the Betar Naval Academy, and it was built and operated with fascist blessings. Many future commanders of the Israeli navy would train here under fascist supervision. The cadets at this academy were supportive of Mussolini’s regime, and supported Italy’s expansionist colonial wars in Africa, most notably the second Italo-Ethiopian war.
The Betar Naval Academy was a Jewish naval training school established in Civitavecchia , Italy in 1934 by the Revisionist Zionist movement under the direction of Ze'ev Jabotinsky , with the agreement of Benito Mussolini . [1] The titular head of the Academy was the Italian maritime scientist Nicola Fusco but Betar leader Jeremiah Halpern ran the School and was its driving force. The Academy trained cadets from all over Europe, Palestine and South Africa and produced some of the future commanders of the Israeli Navy . [1] Civitavecchia fort and harbour today. Although the Revisionists were keen to ensure that trainees avoided local Fascist politics the cadets did express public support for Benito Mussolini 's regime, as Halpern later detailed in his book History of Hebrew Seamanship . [1] Cadets marched alongside Italian soldiers in support of the Second Italo–Abyssinian War and collected metal scraps for the Italian weapons industry. [1] They "felt as if they were living the true Beitarist life in an atmosphere of heroism, militarism, and nationalistic pride." [1] The Academy closed in 1938. [2] The Revisionists and Italy Edit Italy was a source of ideological, historical and cultural inspiration for the Zionist Revisionists of the 1920s and 1930s. [3] The country under Mussolini was seen as a historical reminder of the roots of the Jewish people and as a contemporary example of a once glorious culture reclaiming its role in the world through the affirmation of power and national pride. [3] From the early 1930s onwards Jabotinsky believed that the United Kingdom could no longer be trusted to advance the Zionist cause and that Italy, as a growing power capable of challenging Britain for dominance in the region, was a natural ally. [4] Jabotinsky had been scheduled to meet Benito Mussolini as early as 1922, but for various reasons the meeting did not take place. However, in a letter to Mussolini, Jabotinsky attempted to win his support for the Zionist cause by arguing that for cultural reasons Italy's pro-Arab policy was misguided. [5] Jabotinsky predicted that Italy and the Arabs would inevitably come into conflict and that a Jewish state in the Middle East could act as a buffer between Europe , Asia and Africa . [6] In the second half of the 1920s Revisionism became a growing force among Italian Zionists and the first branch of the movement, the Raggruppamento d'Italia, was founded in 1925. In 1930 the first issues of Leone Carpi's L'Idea Sionistica advanced an anti-British stance and in 1932 the first Revisionist Zionist conference in Italy took place in Milan . [7] Mussolini and the Revisionists Edit In 1933 the Italian foreign ministry (Mussolini was also foreign minister) began circulating internal policy documents arguing that a strong Jewish state would be in Italy's best interests. [8] Although Jabotinsky had still not been able to arrange a meeting with Mussolini it became clear that the Italian government did view the Revisionists as po
There are many more instances where Zionists collaborated with the fascists, and both supported each other’s ideologies. For further reading: Zionist-Nazi collaboration .