Per Prov. 11:30 Etz haChayim is the Torah, which is the fruit of the Tzadiq.
ל פְּרִי-צַדִּיק, עֵץ חַיִּים; וְלֹקֵחַ נְפָשׁוֹת חָכָם.
30 The tree of life is the fruit of the Tzadik; and the Chakham takes souls.
This is explained in Likutei Moharan II, Hosafot Manuscript #5.
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כי התגלות התורה בא מיחודא דאבא ואמא כ"ש שמע בני מוסר אביך ואל תטוש תורת אמך ויחודם
מהעלאות נפשות ישראל בבחי' מיין נוקבין והחכם יכול ליקח הנפשות בבחי' ולוקח נפשות חכם ועי"ז היחוד נולד התורה שהיא עץ החיים וזה בחי' פרי צדיק עץ חיים ולוקח נפשות חכם וכשעולה החכם עם אלו הנפשות בבחי' עיר גבורים עלה חכם ואז ויורד עוז מבטחה ונפש זה בחי' רצון שכל אלו בני אדם הבאים לחכם הדור כל אחד ואחד יש לו איזהו רצון והצדיק לוקח כל הרצונות ועולה עמהם ואח"כ ויורד עוז מבטחה בבחי' והחיות רצוא ושוב רצוא בעליות הנפשות ושוב בחזרת הנפשות עם התגלות התורה
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... For, revelation of the Torah comes of yichud of Aba and Ima, as written, "Hear, my son your father's tradition and forsake not your mother's Torah" (Prov. 1:8). And their unification is from the raisings of the Yisraelite souls, in the aspect of Mayin Nuqvin. And the Chakham is able to take the souls, in the aspect of (Prov. 11:30) "the chakham takes souls."
And this yichud gives birth to the Torah, which is Etz haChayim. And this is the aspect of (ibid.), "The tree of life is the fruit of the Tzadik, and the Chakham takes souls." And when the chakham goes up with these souls in the aspect of (ibid. 21:22), "A Chakham raises a city of the mighty..." and then, "and brings down strength, the trust."
And this soul is the aspect of ratzon, will, as all these people that come to the Chakham haDor, each and every one has some kind of ratzon. And the Tzadik takes all these ratzons and goes up with them. Then he comes down and "brings down strength, the trust."
"And the Chayot run to and fro..." (Eze. 1:14). "Run" in the aspect of raising the souls, and "return" in bringing back the souls with revelation of the Torah. And ...
By the way, thus we see it's on purpose that Rabbi Nachman, held by his followers as the Tzadik haDor (Tzadik of the Era), and his followers, referred to his lessons as "Torahs." Chapters of Likutei Moharan are called Torah Alef, Torah Bet etc. Also he said "I know the source of the Torah from where it comes" etc. etc. Read sifrei Breslev and you will see much more.
Also we have Etz Chayim hi lamchazikim bah.. (Prov. 3:18) etc. etc.