When Jesus says, "I and the Father are one," for example, this could be taken as an exaggerated expression of the proposition that Jesus and the Father are on extremely intimate, or even uniquely intimate, terms, that Jesus is the recipient of mystical graces that he would share with his followers if only they would accept him as standing in this most intimate relation with the Father. Or something along these lines. On this reading, Jesus is not saying that he is literally identical to God, but that he is 'one' with God in perhaps a sense not too different from the sense in which I am 'one' with my wife. One could say that man and wife and 'one flesh' without meaning that they are Siamese twins or that they are literally one and the same.
I am not saying that this is a good interpretation of Scripture; it is beyond my competence to engage in Biblical hermeneutics. I am saying that it is a possible interpretation that shows that the notion that there are exactly three possibilities is dubious. Let us be clear that the question before us is solely whether there is good reason to think that the three-way disjunction, lord or lunatic or liar, is logically exhaustive.