If I remember correctly, Orual considered all three options. She thought "could it really be true", and then " cruel psyche, stop playing this game", and finally "she's completely lost it"... so that's lord (or truth in this case), liar, and lunatic.
You said, "both liar and lunatic options are explicitly denied because Orual sees the god of the mountain." Well, after Psyche snuck a peak at the god of the mountain (causing him to erupt in anger), Orual saw him; but she didn't deny that she saw him did she? Or are you talking about before Psyche snuck in and tried to see the god, when Orual was getting a drink by the river and she thought she saw him?
By the way, I think that Orual really saw the god (while she was getting a drink), and she knows that she really saw him. But she does't want to see the god of the mountain, so she writes things like "tell me, did I really see the god or did I imagine that I did" (that was a rough paraphrase). Remember that Orual is writing the book that we are reading.
I think the whole thing between Psyche, Orual, and the god of the mountain is similar to the situation in real life where one person becomes a believer in God and the other person doesn't. I think this was the point Lewis was trying to make. (That's if you believe he was trying to make a "point" at all; I sometimes wonder if readers [myself included] try to pull too many "points" out of fictional books.) The speech that Orual makes to the gods at the end, when she is finally saying (or the gods are finally making her say) what she "really means", seems to go along with this.