Some random thoughts:

The voice-over at the beginning of the first Superman movie certainly drew parallels between Superman and Jesus--I can't recall the exact words but Jor-El says something like "to you I have sent my only son." It comes through in other parts of that movie too. In Superman II he must sacrifice himself (or at least the life he wants) to save the world. I found the parallel so strong that I was uncomfortable with it.

Although Siegel and Shuster were not Christian, they would have been familiar with the idea of a Messiah. However, I never got that parallel during my limited reading of Superman comics. (Comic books never had enough story in them for me.)

LnC intentionally presents a much more human Superman. I find it interesting, however, that many of the fanfics in the archive present Clark as an extremely charismatic figure, and Superman even more so. Whether or not you believe that Jesus was the Son of God, the historical Jesus must have been an extremely charismatic person to draw the following he did during his lifetime. (As distinguished from those who became Christians based on the accounts of his crucifixion/death/resurrection.) Superman is not, however, without sin. "Superman doesn't lie" except that Clark lies constantly to hide who he is. He also makes human mistakes. And he depends heavily on his human parents for advice--presumably Jesus did not do so. So the comparison falls apart considerably in the version of Superman that so many of us love. But it's a good topic for discussion.