Mishnah Sukkah 3:1
(1) A lulav which was stolen or dried out is invalid.
It teaches this clearly - there is no difference between the first day and the second day of Yom Tov.
Well that makes sense for the dry; we need a beautiful one, and it's not.
What about a stolen one?
Well it does makes sense for the first day, as it says 'to you' i.e. your own. However what about the second day?
Rabbi Yochanan in the name of Rabbi Shimon Ben Yochai
because you can't fulfill a Mitzvah that comes through sin. As it says, "You brought stolen, lame and ill [animals as sacrifices], I [God] am not going to accept that]' (Malachi 1:13)."
Stolen is similar to lame. Just as a lame offering can't be fixed, so too a stolen offering can't be fixed.
It does not matter whether it is before yeiush, or after he despaired.
Well, it makes sense, to say before the owner's despair: "A person, when he brings from his," said the Merciful one, and it (the stolen animal) is not his. But after the owner's despair- hasn't he taken ownership when the owner despaired?
Rather, it is for the reason that it is for him a Mitzvah fulfilled through sin, and Rabbi Yochanan said in the name of Rabbi Shimon the son of Yochai, "What does the verse, 'For I am God, who loves justice and hates thievery greatly' (Isaiah 61:8) mean?
It is compared to an allegory of a flesh-and-blood king, who was passing by a tollbooth and said to his servants, 'Give the tax to the collectors.' They said to him, 'And is not the whole tax yours?' He said to them, 'From me should all the travelers learn, and not distance themselves from the tax.' So too the Holy Blessed One, says, I am God, who loves justice and hates thievery greatly.