In the first chapter, an ape and a donkey find a lion's skin. The ape, Shift, creates a coat for the donkey, Puzzle, out of the skin, and then Shift has the idea to tell people that Puzzle is Aslan. There's a similar premise in one of Aesop's Fables, "The Ass in the Lion's Skin":
An ass found a lion's skin, and dressed himself up in it. Then he went about frightening everyone he met, for they all took him to be a lion, men and beasts alike, and took to their heels when they saw him coming. Elated by the success of his trick, he loudly brayed in triumph. The fox heard him, and recognized him at once for the ass he was, and said to him, "Oho, my friend, it's you, is it? I, too, should have been afraid if I hadn't heard your voice."There's a difference in motivation (in The Final Battle, the donkey is coaxed into the lion's skin where the donkey in Aesop's fable does it of his own volition), but the two are similar. Lewis seems to have used fairy tales in The Chronicles (I wrote about a Grimm fairy tale he seems to use in The Voyage of the Dawn Treader a few weeks ago), so it's likely that he knew and used this element from Aesop too.
In Chapter Seven, Tirian frees a company of dwarfs from some Calormene soldiers. However, they don't join his side and don't even thank him for their freedom. Tirian and his friends walk away, but then one dwarf - Poggin - comes back to join them. "Everyone crowded round him and welcomed him and praised him and slapped him on the back. Of course one single Dwarf could not make a very great difference, but it was somehow very cheering to have even one. The whole party brightened up." I think there are two Biblical references here. The first is Jesus' healing of ten lepers. "When he saw them he said to them, 'Go and show yourselves to the priests.' And as they went they were cleansed. Then one of them, when he saw that he was healed, turned back, praising God with a loud voice..." (Luke 17:14-15). Jesus heals all ten lepers, but only one returns to thank Him; Tirian frees the whole company of dwarfs, but only one returns to join him. Both also have their faith in common. To the one leper who returned, Jesus says, "Your faith has made you well" (verse 19), and Poggin the Dwarf tells Tirian, "I'm on your side, Sire; and on Aslan's." Since Aslan is the Christ-like figure in The Chronicles of Narnia, the faith of both the one returning leper and the one returning dwarf is the same.
The second Biblical story I think this event references is The Parable of the Lost Sheep. Jesus tells a group of people about a man who has one hundred sheep, and after he loses one, he leaves the ninety-nine to look for the one. "And when he has found it, he lays it on his shoulders, rejoicing. And when he comes home, he calls together his friends and his neighbors, saying to them, 'Rejoice with me, for I have found my sheep that was lost.' Just so, I tell you, there will be more joy in heaven over one sinner who repents than over ninety-nine righteous persons who need no repentance" (Luke 15:5-7). The like one sheep that was found, there's Poggin, the one dwarf to return. Similar to the "rejoicing" and "joy" in the parable, Poggin's return is "very cheering" and the party "brighten[s] up."
The rest of the things I noticed are all Biblical references and are all in Chapter Fourteen (Night Falls on Narnia). First, Father Time rises up and blows a horn, ushering in the end of Narnia. In Revelation chapters 8 and 9, the end of the world is also ushered in with trumpets.
Next, the Narnian creatures come up to Aslan and turn either to his left (those who look at him with "fear and hatred") or his right (those who "looked in the face of Aslan and loved him"). There's the same left-or-right separation - the same final judgement - in Matthew 25: "And he will place the sheep on his right, but the goats on the left" (Matthew 25:33). One of those who go to Aslan's right is "one of those very Dwarfs who had helped to shoot the Horses." Earlier, Eustace was indignant about this, but now "he had not time to wonder about that sort of thing... for a great joy put everything else out of his head." This, even more so than the return of Poggin the Dwarf, is the "joy in heaven over one sinner who repents."
Finally, there's the comparison between blood and the sun and the moon:
[The sun] was three times - twenty times - as big as it out to be, and very dark red. ... in the reflection of that sun the whole waste of shoreless waters looked like blood.Similar descriptions are in Revelation 6, at the end of the world: "the sun became black as sackcloth, the full moon became like blood, and the stars of the sky fell to the earth as the fig tree sheds its winter fruit when shaken by a gale" (Revelation 6:12). After Father Time blows his horn in Narnia, there's a shower of falling stars: "these were dozens, and then scores, and then hundreds, till it was like silver rain: and it went on and on."
Then the Moon came up, quite in her wrong position, very close to the sun, and she also looked red.
Clearly, the end of Narnia was inspired by the end of the world as described in the Bible.