Who is actually speaking in these verses?
The psalm does not say. The Min HaMetzar prayer tells how the Gemara hands the verses just before these to David's family. The Gemara keeps going into these lines too. Rashi explains the first pair. The brothers' 'please save' means: save us through David. David's 'please grant success' asks that he succeed as king.
The Midrash Tehillim (a collection of the Sages' teachings on Tehillim) pictures a different scene. The people of Jerusalem speak from inside, and the people of Judah answer from outside. Inside says 'please save,' outside answers 'please grant success.' Inside says 'Blessed is he who comes,' outside answers 'We bless you from the House of Hashem.' They even split one verse: inside says 'Hashem is God,' outside says 'and gave us light.' Then both groups praise God together: 'Thank Hashem, for He is good.'
Rashi, in his commentary on Tehillim, gives more than one reading. On 'I shall not die but live' (118:17) he says the speaker is the people of Israel. He adds that the end of the psalm, from there on, can also be read as about David himself. On 'I thank You' (118:21) he points back to the Gemara: from here on, David, Shmuel, Yishai and the brothers spoke, and 'the one who said this did not say that.'
Why split the lines at all? The Maharal (Rabbi Yehudah Loew of Prague, who died in 1609) says that when God does good, it is not meant for one person, with others gaining by accident. Everyone it reaches was meant to receive it. David becoming king was good for David, for Israel, who now had a king, for Yishai, since the king came from him, and for the brothers, who were close to the royal house. Each owed his own thanks, so each has his own lines. At the end, everyone thanks God together, because it all came from one act.
The sources do not pick a winner. The Gemara hears one family, each with his own line. The Midrash hears two crowds answering each other, one inside and one outside.
Pesachim 119a with Rashi,Midrash Tehillim 118:22,Rashi on Tehillim 118:17, 118:21 and 118:27,Maharal, Gevurot Hashem, chapter 64What does it mean to 'tie up' a festival with ropes?
The verse says: 'Isru chag ba'avotim ad karnot hamizbeach.' Word for word: tie the festival with thick ropes, up to the horns of the altar. It sounds like an order to tie up a holiday.
The simplest reading is about animals. Rashi says the festival offerings, clean and checked for blemishes, were tied by the people to the legs of their beds until they brought them to the Temple courtyard, to the corners of the altar. Radak (Rabbi David Kimchi, a Bible commentator in Provence, about 1200) pictures a lamb bound with ropes until it reaches the altar. So 'chag' here is the festival offering.
The Gemara reads it another way. Rabbi Abbahu says in the name of Rabbi Elazar: anyone who takes a lulav in its binding, and a myrtle branch with its thick leaves, is counted as if he built an altar and offered a sacrifice on it. Now the verse is about the bundle in your hand.
Then the Gemara reads 'isru' as 'issur,' a tie. Anyone who makes a tie to the festival by eating and drinking is counted as if he built an altar. Rashi explains it as the festival itself, a time of pleasure in food and drink, and adds that some say it means the day after the festival.
That is where Isru Chag, the day after a festival, comes from. The Rema (Rabbi Moshe Isserles of Poland, 1500s, whose notes on the Shulchan Aruch record Ashkenazi custom) writes that people customarily eat and drink a bit more on that day, and it is called Isru Chag.
So one short line carries three pictures: a lamb on a rope, a bundle of branches, and a day of extra food. The Sages give the last two the same credit. It counts as if you built an altar.
Tehillim 118:27,Rashi and Radak on Tehillim 118:27,Sukkah 45a-45b with Rashi,Rema on Shulchan Aruch, Orach Chaim 429:2Why ask for two things? If God saves me, isn't that enough?
The verse asks twice: "Hashem, please save," and then "Hashem, please grant success." If you have been saved, what is left to ask for?
Malbim (Rabbi Meir Leibush, a Bible commentator in Eastern Europe in the 1800s) says everyone is praying for two separate things. First, that God save them from the enemy. Second, that He make them succeed in everything they do from now on. Rescue ends a danger. Success is about what you do with the days after it.
Radak (Rabbi David Kimchi, a Bible commentator in Provence, about 1200) hears a different speaker and a different target. Israel say it for everyone who comes under God's shelter and returns to serve Him, and the priests in the Temple say it for everyone who comes to serve. So the request is not only about me. It is about whoever is walking in.
Ibn Ezra (a Bible commentator from Spain, 1100s) ends his comment by putting the verse in his own words: Hashem, save now, and grant success now. Metzudat David (a commentary on the Prophets and Writings from the 1700s) reads it the same way. So the little word "na," which we usually translate "please," is read here as "now": a request for today.
These readings do not agree on who is speaking or who is being prayed for. Only the Malbim takes on the question directly: being saved and succeeding are two separate gifts, and the verse asks for both.
Malbim on Tehillim 118:25,Radak on Tehillim 118:25,Ibn Ezra on Tehillim 118:25,Metzudat David on Tehillim 118:25