Gemara

(Mishnah - R. Meir): We may seek to permit a vow by saying 'had you known that through this vow you transgress "Lo Sikum", "Lo Sitor"... would you have vowed?!'

Yoma 22b: A true Chacham must take vengeance like a snake.

Question: It says "Lo Sikum" and "Lo Sitor"!

Answer: These apply to monetary matters:

(Beraisa): An example of vengeance: Reuven refused to lend a scythe to Shimon. The next day, Reuven asked to borrow an axe, and Shimon said 'I won't lend to you, just like you didn't lend to me.'

An example of bearing a grudge is if Shimon refused to lend an ax to Reuven, and the next day Shimon asked to borrow a garment, and Reuven said 'Yes. I am not like you, who refused to lend to me!'

Question: Also regarding Tza'ar ha'Guf, it is proper not to take vengeance!

(Beraisa): "V'Ohavav k'Tzeis ha'Shemesh bi'Gvuraso" refers to one who is disgraced and does not disgrace. People shame him and he does not answer...

Answer: A Chacham bears a grudge in his heart. (He does not avenge, but he allows others to avenge for him.)

Rosh Hashanah 17a: If one overcomes his Midos (does not mete out to others like they did to him), all his transgressions are overlooked.

Megilah 28a: One of the merits to which R. Nechunya ben Hakanah attributed his long life was that he did not sleep before forgiving one who had cursed him.

This is like Mar Zutra, who would forgive all who wronged him before going to sleep.

Rishonim

Ritva (Yoma 23a DH Omar): The Gemara discussed different Kelim to teach that the Lavim apply even when the first borrower refused to lend a Keli worth less than what he borrowed. Alternatively, the Gemara gives a typical case in which he asked to borrow a different Keli than he lent.

The Rif and Rosh bring the Mishnah in Nedarim.

Rosh (65b DH she'Hayisa): The case is, Reuven vowed not to lend Kelim to Shimon because Shimon refused to lend to Reuven.

Rambam (Hilchos De'os 7:7): One who takes vengeance transgresses the Lav of Lo Sikum. Even though he is not lashed, it is a very bad attitude. Rather, a person should overlook all worldly matters (in which he was wronged). People of understanding know that such matters are folly and not worth avenging. An example of vengeance: Reuven refused to lend an ax to Shimon, and when Reuven later asked to borrow an axe, Shimon said 'I won't lend to you, just like you didn't lend to me.' Rather, Shimon should lend to him willingly and not respond the way Reuven treated him.

Rambam (8): Similarly, one who bears a grudge against a Yisrael transgresses the Lav of Lo Situr. For example, Shimon refused to rent a house to Shimon or to lend him an ox, and later Shimon needs to borrow or rent from Reuven, and Reuven says 'Yes. I am not like you, and I will not treat you like you treated me!' As long as he bears resentment he is prone to take vengeance. Rather, he must erase the matter from his heart. This is the proper Midah that enables settlement of the world and interpersonal relations.

Kiryat Sefer: Mid'Oraisa, Lo Sikum v'Lo Sitor apply only to lending things. Regarding words or Midos, they are only mid'Rabanan.

Rosh (Bava Kama 3:13): If two bulls or people started fighting together, or if one damaged the other and later the victim retaliated, the one who did more damage pays for the excess. If one started the fight, he pays and the other is exempt. Regarding people, we do not say 'if one did improperly, and another did improperly to and harmed him, he is exempt.' Nevertheless, a person may fight back if he has no other way to save himself.

Sha'arei Teshuvah (3:38): The punishment for Lo Situr is not for the words, rather, for bearing the grudge in his heart. The Isur applies only to grudges for monetary matters. One may bear a grudge for offenses of haughtiness, contempt and seeking to do evil.

Sefer ha'Chinuch (Mitzvah 241): One may not take vengeance against a Yisrael for any harm or pain. Most people seek to return the harm or hurt they suffered at the hands of others. "Lo Sikum" forbids this. One must put to his heart that everything that happens to him is from Hash-m; all suffering was decreed because of his sins. When Shim'i ben Gera cursed David, David said 'Let him curse. Hash-m told him to!' One who decides to hate someone because he did evil to him transgresses this Lav. One is not lashed for it because one can transgress without an action.

Be'er Mayim Chayim (introduction to Chafetz Chaim, Lavim 8-9): Sefer ha'Chinuch forbids avenging or bearing a grudge after one was insulted. However, the Chinuch himself (Mitzvah 338) says 'one is not commanded o be silent to one who insults him. It is impossible for a person to be like a rock. Further, this would be like admission to the insults.' One may retaliate at the time he is insulted; it is a praiseworthy Midah not to.

Poskim

Shulchan Aruch (YD 228:10): If Reuven vowed not to lend Kelim to Shimon or to greet him, we may seek to permit it by saying 'had you known that through this vow you transgress Lo Sikum and "do not hate your brother in your heart", would you have vowed?!'

Shulchan Aruch (CM 421:13): If Reuven started hitting Shimon, Shimon may hit back to save himself.

Rema: Similarly regarding insults, the one who started pays the fine.

Source (Darchei Moshe, citing Or Zaru'a): The Torah anticipates that a Go'el ha'Dam will try to kill the Rotze'ach - "Ki Yecham Levavo" (Devarim 19:6; it is human nature to retaliate immediately). Similarly, if Reuven hit Shimon or called him a thief, and Shimon called Reuven a Mamzer, Shimon is exempt.

SMA (24): We must make a small correction in the text of the Tur and Shulchan Aruch. If not, it suggests that if Reuven hit Shimon and ceased, and Shimon hit back amidst rage he is liable. There is no source for this; we learn the laws of people and animals together, and regarding animals the victim is exempt for retaliating as long as it is enraged.

Rebuttal (Taz DH v'Chozar): We need not change the text. The Tur and Shulchan Aruch teach that immediately after the instigator finished his deed, if the victim hits back he is liable.

Chafetz Chaim (introduction, Lavim 8-9): If Reuven hates Shimon because Shimon did not help him, e.g. to lend to him money, and Reuven later sees something lowly in Shimon and publicizes it, he transgressed Lo Sitor immediately, and "Lo Sikum" when he spoke.

Be'er Mayim Chayim (ibid., citing Yere'im): These Lavim are written near verses discussing monetary laws. We are commanded not to avenge a refusal to give Tzedakah or any monetary Chesed, or to bear a grudge for this. One who enjoys hearing Lashon ha'Ra about one who refused to help him also transgresses "Lo Sikum v'Lo Sitor". Even though the Gemara says that these Lavim apply only to monetary matters, but regarding Tza'ar ha'Guf one may bear a grudge, he may not speak Lashon ha'Ra about the abuser. Even if the Lav of Lashon ha'Ra would not apply to him, he would cause the listeners to transgress. It is not clear if one may take monetary vengeance for Tza'ar ha'Guf.

Question: Sefer ha'Chinuch holds that the Lavim apply even to Tza'ar ha'Guf. It seems that the Rambam agrees, for he does not distinguish. The Gemara in Yoma says that the Lavim apply only regarding monetary matters!

Answer (Be'er Mayim Chayim ibid. DH Aval; also see Erech Apayim ibid. DH Hinei): They must say that when the Gemara asked from "V'Ohavav k'Tzeis ha'Shemesh..." and answered that a Chacham bears a grudge in his heart, it retracted from the distinction between Tza'ar ha'Guf and monetary matters.

Be'er Mayim Chayim (ibid.): It is a Safek mid'Oraisa whom the Halachah follows, so we must be stringent in every case.