Gemara

Beraisa - R. Bena'ah: If one learns Torah Lishmah, it becomes an elixir of life for him - "Etz Chayim Hi la'Machazikim Bah"...

If one learns Torah Lo Lishmah, it becomes a lethal poison for him - "Ya'arof k'Matar Likchi";

Arifah refers to killing - "V'Orfu Sham Es ha'Eglah".

Pesachim 50b - Contradiction (Rava): It says "Ki Gadol Ad Shomayim Chasdecha", and it says "Ki Gadol me'Al Shomayim Chasdecha"!

Answer: Hash-m's Chesed is above Shomayim for those who serve Him Lishmah. It is up to Shomayim for those who serve Lo Lishmah.

Rav Yehudah: A person should always engage in Torah and Mitzvos even Lo Lishmah, for this will lead him to do them Lishmah.

Sotah 47a - R. Chanina: Because of the 42 sacrifices that Balak brought, 42 youths of Yisrael died (when Elisha incited bears on them).

Question: But Rav Yehudah taught that Balak's reward was that Rus descended from him, and from her Shlomo - "Elef Olos Ya'aleh Shlomo"!

R. Yosi ben Choni: Rus was the (grand)daughter of Eglon Melech Mo'av, who was the son of Balak.

We learn from Balak that a person should always engage in Torah and Mitzvos, even Lo Lishmah, for this will lead to Lishmah!

Answer: Balak's intention was to curse Yisrael (to diminish them).

Berachos 17a - Rava: "Reishis Chachmah Yir'as Hash-m Sechel Tov l'Chol Oseihem" - it does not say 'l'Osim', rather, "l'Chol Oseihem", to those who do Mitzvos Lishmah;

If one learns Lo Lishmah, it would have been better if he had not been created.

Rishonim

Rashi (DH Lishmah): Lishmah is "Ka'Asher Tzivani Hash-m Elokai", not to be called 'Rebbi'.

Question: In Ta'anis and Berachos, it says that learning Lo Lishmah is terrible. In Pesachim it is encouraged, for it leads to Lishmah!

Answer #1 (Tosfos Sotah 22b DH l'Olam): In Pesachim it refers to one who learns from fear of punishment or in order to get reward. In Ta'anis and Berachos it discusses one who learns without intent to fulfill the Mitzvos. His learning causes that he transgresses b'Mezid instead of b'Shogeg.

RaDA(Ayen) (brought in Likutim in Frankel Rambam Talmud Torah 3:5): This Tosfos forbids learning in order to be called Rebbi.

Answer #2 (Tosfos Ta'anis 7a DH v'Chol and Berachos 17a DH ha'Oseh): In Pesachim it refers to one who learns in order to be called Rebbi, or to be honored. In Ta'anis and Berachos it discusses one who learns in order to quarrel.

Question: We learn the greatness of Lo Lishmah from Balak, and he served in order to curse Yisrael, which is like in order to quarrel!

Answer (Maharsha Horayos 10b DH she'Mitoch): Balak did so only because he feared Yisrael. Therefore this is like serving out of fear, which leads to serving Lishmah.

Rambam (Hilchos Talmud Torah 3:5): A person is judged first about Divrei Torah, and then about his deeds. Therefore, Chachamim taught that a person should always learn Torah even Lo Lishmah, for this will lead him to learn Lishmah.

Question: Why does the Rambam say 'therefore, one should always learn Lo Lishmah?' The Gemara says that one should always engage in Torah and Mitzvos Lo Lishmah in order to get to Lishmah, even though the first judgment is not about other Mitzvos!

Answer (Binyan Shlomo, brought in Likutim in Frankel Rambam): The Gemara did not distinguish different kinds of Lo Lishmah. The Rambam infers that all are the same. If one learns Lo Lishmah, it is fitting that he was not created. Nevertheless, it is better to learn Lo Lishmah than not to learn at all, for from Lo Lishmah he will come to Lishmah. Other Mitzvos do not normally lead to honor or wealth. The only Lo Lishmah that applies to them is in order to receive reward. Surely, this is permitted. We cannot say that it is fitting that one who serves this way was not created! Therefore, the Rambam did not discuss doing Mitzvos Lo Lishmah. Alternatively, one who does Mitzvos Lo Lishmah does not transgress, but one who learns Lo Lishmah transgresses. Nevertheless, it is better to learn Lo Lishmah, for the punishment for Bitul Torah is very great, and one must make all efforts to reach learning Lishmah. Perhaps 'one is judged first about Divrei Torah' refers to Bitul Torah, which is worse than learning Lo Lishmah, therefore it is better to learn Lo Lishmah.

Rambam (Hilchos Teshuvah 10:1,5): One should not do Mitzvos and learn in order to receive the Berachos written in the Torah or to get the world to come. One should not refrain from Aveiros to avoid the curses in the Torah or to prevent being cut off from the world to come. This is not how Chachamim serve Hash-m. Rather, this is how we teach children, women and Amei ha'Aretz until they become wiser. Then, we gradually reveal to them this secret that one should serve purely out of love and habituate them to do so.

Rambam (2): This level of serving out of love is very high, and not every Chacham merits it. It is the level of Avraham. He is called "Ohavi" because he served out of love. We are commanded to do so - "V'Ohavta Es Hash-m Elokecha b'Chol Levavcha uv'Chol Nafshecha uv'Chol Me'odecha". When one properly loves Hash-m, immediately he will do all Mitzvos out of love.

Rambam (4): Great Chachamim privately taught to their sharp Talmidim not to serve like slaves who anticipate recompense. Rather, serve like slaves who serve without any intent for recompense, rather, because it is fitting to serve the Master, i.e. out of love.

Rambam (5): If one learns in order to get reward or avoid punishment this is Lo Lishmah. If one learns not because of reward or punishment, rather, out of Ahavas Hash-m, this is Lishmah. Chachamim taught that one should always engage in Torah even Lo Lishmah, for from Lo Lishmah he will come to Lishmah.

Lechem Mishneh (Talmud Torah 3:5): The Rambam did not explicitly distinguish between different kinds of Lo Lishmah. However, it appears that everyone must distinguish like Tosfos in order to answer Tosfos' question.

Birkei Yosef (YD 246:20): The Rambam distinguishes in Hilchos Teshuvah. He says that learning for wealth, honor or reward is Lo Lishmah, and says that one should always learn Lo Lishmah... Other forms of Lo Lishmah, i.e. to quarrel, are forbidden. Chachamim would not condone them.

Teshuvas Rambam (445 in Blau Edition): There is no contradiction between the teachings regarding Torah Lo Lishmah. The Mitzvah is to learn Lishmah. If one learns Lo Lishmah, it is fitting that he was not created. Nevertheless, it is better to learn Lo Lishmah than not to learn at all, for from Lo Lishmah he will come to Lishmah. see Sefer ha'Michtav Hotza'as Sofer p. 426

Poskim

Shulchan Aruch (YD 246:20): One should always engage in Torah and Mitzvos even Lo Lishmah, for this will lead him to Lishmah.

Mishnah Berurah (138:5): When the Shali'ach Tzibur reads Berachos (or curses) in the Torah, he may not intend for them to be fulfilled on himself (or others). He must read Lishmah, without any other intent.

Ben Ish Chai (2:Parashas Nasa): Normally, one may request only one thing at a time from Hash-m. However, if one learns Lishmah, all of his requests are in order to serve Hash-m, so even many requests are considered like one.

Acharonim

Even Shleimah (8:2): One should always engage in Torah and Mitzvos even Lo Lishmah, for this will lead him to Lishmah. This refers to one who has no intent, he merely follows his family's practice, but not if his learning is primarily to get honor. Also, if one's Yetzer incites him not to learn at all, and he is unable to overcome it to learn Lishmah, he should begin to learn Lo Lishmah, and he will come to learn Lishmah.

Gra (on Mishlei 25:21): "Im Ra'ev Sona'acha Ha'achilehu Lechem" refers to the Yetzer ha'Ra. 'If the despicable one confronts you, lead him to the Beis Medrash' (Sukah 52b) refers to the Yetzer ha'Ra inciting one not to learn at all. If one cannot overcome it to learn Lishmah, he should begin to learn Lo Lishmah. Since he wants to reach Lishmah, he will come to learn Lishmah.

Nefesh ha'Chayim (Perakim 2,3 (after Sha'ar 3)): The Zohar teaches that one who engages in Torah, even Lo Lishmah, is rewarded with wealth, honor and serenity in this world, and will not be judged in Olam ha'Emes - "Orech Yomim bi'Minah bi'Smolah Osher v'Chavod". This is as long as he does not learn in order to quarrel. The Gemara says that since humility Lishmah is greater than rebuke Lishmah, also humility Lo Lishmah is greater. Likewise, just like Torah Lishmah is greater than all the Mitzvos, also Torah Lo Lishmah. Even if one always learns Lo Lishmah, surely at some moments he is Lishmah. This is Mekadesh the entire learning.