Why does it say "Lo Lanu"?
Rashi: Not due to us and our proper deeds should You do for us.
Radak: Just like You did Chesed with our fathers, and took them out of Egypt even though they were not worthy, only for honor of Your name and Bris Avos - so do with us in every generation!
Radak citing Pesachim 118a #1: This refers to subjugation by the [four] kingdoms.
Radak: Chazal (Pesachim 117a) gives several opinions about who said this [first]. Refer to 113:1:1:1-6.
Pesachim 118a #2: This refers to the war of Gog and Magog.
Malbim: It said above (114:2) "Yisrael Mamshelosav." Hashem showed His authority to rule over nature and do wonders via Yisrael. This does not apply nowadays - we are not worthy to sanctify His name like Yehudah was.
Why it "Lo Lanu" repeated?
Radak: This is to strengthen the matter.
What will honor Hashem's name?
Rashi: The Goyim will not say "where is their G-d?" (verse 2).
Malbim: You already put Your name on us, that You oversee Yisrael and do miracles for them. Now You must give honor to Your name, to avoid Chilul Hashem.
What is the meaning of "Al Chasdecha Al Amitecha"?
Radak: It is as if it says v'Al Amitecha. Similarly, [the prefix Vov is omitted in] "Shemesh Yare'ach" (Chabakuk 3:11). Do with us, like You do Chesed with all creations, and more, due to Your Emes, to fulfill Your word that You swore to our fathers.
Malbim: You must do either due to Chesed, without merit or promise, just like the beginning of the miracles was due to Chesed, or due to Emes and the promise that You will be Elokim to us.