I think the wording they use may have been "spiritual" .... and other than a possible sense of your spirituality with nature or something like that, yes, they're really looking for a religious letter. The drop down box for selecting your variety of spirituality on the secondary application site actually had a ton of different selections with much more variety than I had expected.
No you are not required to have a LOR from a spiritual leader. Though it is preferred, they have given interviews to people who don't have LOR's from a spiritual leader. If you don't have an LOR from a spiritual leader i'm pretty sure there's an option to somewhere on the app to mark that you don't have an LOR from a spiritual leader... If you do decide to do that make sure you have a reason for not having one and such... i think my cousin applied last cycle and he wrote a letter to LLU telling them why he didn't have a letter. He still got an interview from them.
Well that's interesting, I had heard otherwise, but I guess there's always exceptions? I'm hoping that LLUProf can give us a solid answer on the question if a Religious Letter is usually required or not.