Gemara

29b - Mishnah: A stolen Lulav is Pasul.

Question: The Mishnah disqualifies without distinction, i.e. even after the first day when it need not be "Lachem", i.e. yours. What is the reason?

Answer #1 (R. Yochanan citing R. Shimon, and R. Ami): It is Mitzvah ha'Ba b'Aveirah:

"And you offer (an animal that is) stolen, lame or sick" - this equates a stolen animal to a lame one. Just like a lame animal cannot become acceptable, also a stolen animal, even after Yi'ush (when the owner despairs of getting it back)!

Question: Granted, it is invalid before Yi'ush - "Adam Ki Yakriv Mikem Korban", and this is not his. But why is it invalid after Yi'ush? The robber acquires through despair!

Answer: It is invalid because it is Mitzvah ha'Ba b'Aveirah.

Answer #2 (R. Yitzchak bar Nachmani citing Shmuel): The Mishnah discusses Yom Tov Rishon. On Yom Tov Sheni one is Yotzei with Gazul, just like he is Yotzei with borrowed Minim.

Rav Huna (to Hadasim vendors): When you buy Hadasim from Nochrim, do not cut them yourselves. Let the Nochrim cut them and give them to you.

This is because Stam Nochrim steal land, and land cannot be stolen (even after Yi'ush it belongs to the original owner). If they cut the Hadas, the owners Yi'ush takes effect when it is in the Nochri's hands, and there will be Shinuy Reshus when you get it (so you acquire).

Question: Even if the vendor would cut it, there would be Yi'ush in the vendor's hands, and Shinuy Reshus in when the buyer gets it!

Answer: Rav Huna's advice is needed for the Hadasim that the vendors themselves will use.

Rishonim

The Rif brings the Mishnayos which disqualify stolen Minim.

Ba'al ha'Ma'or (14b): Many Ge'onim rule like R. Yochanan in the name of R. Shimon, who disqualifies stolen Minim even after the first day due to Mitzvah ha'Ba b'Aveirah. This is difficult, for R. Yochanan himself holds that a thief is liable before and after Yi'ush. This shows that Yi'ush by itself (without Shinuy Reshus) does not acquire! Shmuel, who holds that one is Yotzei on Yom Tov Sheni, and Rav Huna, who instructed the Hadasim vendors, are not concerned for Mitzvah ha'Ba b'Aveirah!

Rebuttal (Hasagos ha'Ra'avad): Rav Huna instructed the vendors to let the Nochri cut the Hadasim to avoid Mitzvah ha'Ba b'Aveirah! Old texts disqualify an Asherah (even not of Moshe) on the second day due to Mitzvah ha'Ba b'Aveirah. This is only regarding Hadasim, for one gets Hana'ah from their smell.

Ba'al ha'Ma'or: Rav Ashi (note - our texts say Rava) answered for Shmuel, and he is Basra. There are two versions about an Esrog from which mice ate (36b). The Rif says that we are lenient, for it is a Safek mid'Rabanan after the first day. The Ritz Gei'us learns from the Yerushalmi that all the Pesulim (Shemen la'Ma'or - including Gazul) apply only on the first day.

Rebuttal (Milchamos Hash-m): The Halachah normally follows R. Yochanan against Shmuel, all the more so here because he cites a Tana, and R. Ami agrees with him. Whenever a Chacham cites someone but disagrees, the Gemara says so. The simple reading of the Mishnah supports R. Yochanan. Later Amora'im often answer to defend opinions they oppose.

Rambam (Hilchos Lulav 8:1): If one of the four Minim was Gazul or Ganuv (stolen openly or stealthily), it is Pasul, even after Yi'ush.

Magid Mishnah: The Gemara explicitly disqualifies even after Yi'ush.

Question: R. Yochanan disqualifies even after Yi'ush, but the Rambam disqualifies only on the first day (see Halachah 9 below). This is like R. Yitzchak, who does not disqualify because of Mitzvah ha'Ba b'Aveirah!

Answer #1 (Kesef Mishneh): The Rambam holds that Yi'ush by itself Eino Koneh, so it is not "Lachem".

Answer #2 (R. Mano'ach and Lechem Mishneh): Even R. Yitzchak is concerned for Mitzvah ha'Ba b'Aveirah, but only on the first day when Lulav is mid'Oraisa even outside the Mikdash.

Rambam (9): The Pesulim due to Mumim, Gazul or Ganuv apply only on the first day. After this they are Kesherim.

Rebuttal (Ra'avad): Not all agree about stolen or dry Minim. Stolen Minim are Pasul because of Mitzvah ha'Ba b'Aveirah.

Rosh (3:3): The enactment to take the Minim all seven days is like the mid'Oraisa law. R. Shimon holds that we enacted to disqualify Gazul all seven days because of Mitzvah ha'Ba b'Aveirah. Shmuel holds that since it is mid'Rabanan we did not disqualify it. Even though the verse of Mitzvah ha'Ba b'Aveirah discusses a Korban, it applies to all Mitzvos, like we find regarding Chalah (Bava Kama 94a). Shmuel holds that it applies only to mid'Oraisa laws. This is unreasonable. Since he blesses with Hash-m's name, this reviles Hash-m even regarding mid'Rabanan Mitzvos! A question was asked against Shmuel and a poor answer was given. We do not rely on it.

Rosh and Ran (13b DH ul'Inyan): The Rif brought the Mishnah without the argument of the Amora'im. This implies that he holds like the Gemara's initial understanding of the Mishnah, that it is Pasul on all days.

Tosfos (30 DH Ha) and Ran (ibid.): Mitzvah ha'Ba b'Aveirah applies only if he never acquired it, or if he acquired it through doing the Mitzvah. It does not apply if he acquired it before the Mitzvah. The Gemara (94a) suggests that even after acquiring through Shinuy, one may not bless due to Mitzvah ha'Ba b'Aveirah. This is a mere Dichuy. Alternatively, we are more stringent about a Berachah.

Poskim

Shulchan Aruch (OC 649:1): If any of the four Minim was stolen openly or stealthily, it is Pasul, before or after Yi'ush.

Kaf ha'Chayim (5): Most Poskim say that Mitzvah ha'Ba b'Aveirah applies even to theft mid'Rabanan, e.g. taking something that a child found.

Shulchan Aruch (ibid.): However, if one stole it and acquired it before the Mitzvah, for example he stole a Lulav and trimmed it it is Kosher because he acquired it through Shinuy.

Source (Gra DH Aval): One who stole wood and built a Sukah is Yotzei if he acquired it beforehand through Shinuy (31a). A Lulav of an Asherah is Pasul because of Kesusei Michtas Shi'urei, not due to Mitzvah ha'Ba b'Aveirah.

Mishnah Berurah (4): We must say that it was not called a Lulav until he trimmed it, so there is Shinuy ha'Shem.

Kaf ha'Chayim (11): Shinuy Ma'aseh acquires even before Yi'ush (CM 362:1). The Levush requires Yi'ush before the Shinuy; it is not clear why.

Shulchan Aruch (ibid.): However, he may not bless on it.

Mishnah Berurah (10,12): The Isur to bless is only if it was surely stolen. Conquest in war is a proper acquisition.

Shulchan Aruch (ibid.): Some say that it is Pasul only for the thief, but it is Kosher for others after the first day.

Gra (DH v'Yesh): Orchos Chayim says that even before Yi'ush Mitzvah ha'Ba b'Aveirah applies only to the thief. The Yerushalmi says that Mitzvah ha'Ba b'Aveirah is no Mitzvah because the advocate prosecutes. This does not apply to when the one doing the Mitzvah did not transgress.

Mishnah Berurah (8): The Magen Avraham disagrees with this. Even though one may rely on the lenient opinions, one may not bless.

Rema: One (who buys Minim from a Nochri) should let the Nochrim detach them. This is because Stam Nochrim steal land, and land cannot be stolen.

Magen Avraham (6): If the Yisrael who cuts it gives to another Yisrael, this is fine.

Mishnah Berurah (9): Yi'ush does not help to acquire until it is detached, for while it is attached it is like land.

Shulchan Aruch (ibid.): There is no distinction between Eretz Yisrael and Chutz la'Aretz.

Magen Avraham (7 and 637:3): Rashi (Sof 30a) says that Stam Nochrim steal land from Yisrael. Even though we hold that it is forbidden to steal from Nochrim, this would not be called Mitzvah ha'Ba b'Aveirah. The Shulchan Aruch is concerned even for land stolen from a Nochri. The Rashba says that Rashi was not precise, because we hold that it is forbidden to steal from Nochrim. The Yere'im say that even the opinion that permits Gezel Nochri would forbid here, for it is not "Lachem".

Kaf ha'Chayim (21): Some say that the same applies nowadays. Others say that nowadays the Yisrael may cut because Nochrim acquired through conquest in war. If a Nochri has a document valid according to the law of the kingdom, it is legally his. Others dispute this, because judges take bribes. Today government officials (not judges) are appointed over this and they investigate properly. Nevertheless, it is better to let the Nochri cut it.

Shulchan Aruch (5): The Pesulim because of Mumim or open or covert theft apply only on the first day. After this they are Kesherim.

Magen Avraham (15): In Sa'if (1), the Shulchan Aruch disqualified Gazul all seven days! Perhaps that is only l'Chatchilah for the thief himself, but others are permitted.

Rebuttal (Bi'ur Halachah DH Mipnei): 'Pasul' connotes even b'Di'eved! Rather, here the Shulchan Aruch merely copied the Rambam's words (like it often does).

Rema: Some forbid stolen Minim all seven days. This is our custom.