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,...

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.