[1) Incidentally, the tree mentioned in the Gemara 15a never acted as a lechi. It is mentioned by the Gemara when the Gemara thought that just like Abaye and Rava were arguing about a lechi they were also arguing about a mechitzah, so the question was is the tree considered as a mechitzah or not].

2) However it is true that a tree can be a lechi. This is stated by the Rashba, cited by the Magid Mishneh on Rambam Hilchos Eruvin 17:22, who writes that if there was no other lechi specifically placed in the mavui as a lechi, or even if there was a special lechi but it fell down before Shabbos commenced, then the tree permits the mavui as a lechi does.

3) The reason for this is implied by the first Rashi on 15a and the Beis Yosef explains how we see this. Rashi writes that a lechi standing on its own means that the lechi was not fixed there in order to equip the mavui, and was not prepared for this purpose. Beis Yosef; on the Tur Orach Chaim 363:11 DH vAfilu; and cited by the Rema in Shulchan Aruch 363:11, writes that Rashi is telling us that one does not require intention before Shabbos to rely on it, but if there was no other lechi there before Shabbos, this is equivalent to relying on it before Shabbos. This is because we assume that a person knows that a mavui needs a lechi, so if the only item there that could be thought of as a lechi is the tree, then it must be that the people in the mavui want the tree to be a lechi. Even though a tree does not look like a standard lechi, that does not disturb us, because the Halacha is that the lechi must be 10 tefachim high with no minimum thickness or width, and the tree meets these requirements.

4) On 5a, when you added on to a wall of 4 amos, there is a different reason that it is not a lechi. This is because it is too big. Since the lechi is 4 amos it could itself be a mavui in its own right. This is stated by Rashi 5b DH D' Amos and Mishneh Berurah 363:40.

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