Similarities between The Hobbit and The Lion, the Witch and the Wardrobe - and how they both present Christianity.
I need to know a few motifs, themes, and symbols. What I don't understand is how they both present Christianity. I know that Aslan represents Jesus, but how about The Hobbit?
I have to say that I don't necessarily think that Tolkien intended to use this novel to present Christianity in the same way that Lewis did with The Lion, The Witch and the Wardrobe. Of course, reading this latter novel clearly presents us with an allegory of Christianity - Aslan, as you identify, represents Jesus who willingly gives his life up for someone unworthy (Edmund) and then is resurrected as a result to defeat the forces of evil, encapsulated in the white witch. However, if we consider The Hobbit in these terms, there are no easy allegories that stand out. In fact, it is important to remember that Tolkien himself deliberately eschewed allegorical readings of his work. Thus although he was a Catholic and an important friend of C. S. Lewis, it is important not to try and read too much into his work and come up with meanings that are not there.
The one theme that is similar to both is the theme of good vs evil and how it is resolved. Both then present us with a simplistic world in which characters are easily slotted into one of two categories: good or evil. Thus dwarves, hobbits, men and elves are good and goblins and Wargs are evil. There is also the eventual triumph of good over evil. However, in The Hobbit there is a blurring of these boundaries, for example consider Thorin's questionable actions and decisions when he is suffering from gold greed or The Master of the Lakeland People. Also, you might want to think about the whole pretext of the adventure - robbery. Even though Smaug took the treasure from the dwarves originally, he had added to it from other sources, which the dwarves are planning to "appropriate" into their own treasure. Somewhat questionable.
So, in conclusion, I don't think we can treat these two novels in the same way. One is clearly a Christian allegory, whereas, to my mind at least, Tolkien seems intend on creating a mythical world loosely based on Norse and Anglo-Saxon mythology and peopling it, creating an updating of so many of these old myths.
Both of the novels carry a few similarities that can be then tied back to biblical allusions and Christian motifs.
Answering your call: The most clear relation to Christianity is the hero who takes on the self-less task for the very purpose of helping others. Bilbo gives up his possessions and comfort, which he very much enjoys, to take his journey. In The Lion the Witch and the Wardrobe, the children, even thought they do not first enter the forest for this reason, soon go on a journey to rescue Tumnus.
They both follow the traditional "hero's journey" by receiving their call to action and then taking it. This has a clear connection or "message" that reflects the Christian philosophy to respond to your own calling despite the potential harms or trials you could face.
Good vs. Evil: A more loosely related theme might be to simply cite the battle between good and evil.
Good vs. Evil- Rejecting Greed and Sin: Beyond the surface battles against the villains in the stories, there is also the internal battle against evil. Both text show the internal conflict of characters as they struggle battle the earthly urges such as greed.
One example would be Edmund in The Lion the Witch and the Wardrobe. When he first enters Narnia, he is overcome by a desire to eat and eat the turkish delight. While this is clearly the work of magic, when he returns home he then refuses to side with Lucy because of his desire to return to the Witch. Edmund is not able to see the Witch as evil and is overcome by his greed. It is then Aslan, who is frequently compared to Jesus, that must help to save Edmund from the trouble his greed gets him into.
The theme of greed runs rampant through The Hobbit. Bilbo's final acceptance to take the journey is based upon his promise of treasure. The dwarves are taking the entire journey to seek out treasure and treasure is the main rift between the dwarves and the elves. The ultimate message at the end is that the treasure was not the reward and that simplicity is. The small amount of treasure brought home at the end is then spent on his relatives. In the end, Bilbo continues to lead a very simple life which shows that it is important not to let greed overtake you.
Bilbo is willing to sacrifce all his share of the gold to avoid war and spares Gollum's life despite the fact Gollum wanted to eat him, these are christ-like actions.