Imagine that I borrowed that other person's red cup, showed it to Lox and said, " I have got a red cup. Do you like it?"

Got you:

Keith: Do you like my (meaning the cup I borrowed from an expert on red cups) red cup?

Lox: No. I don't like your cup as it's faulty. Look, the handle's falling off and it's leaking.

Keith: It isn't MY (meaning personal ownership) cup and in any case the person I borrowed it from knows more about cups that you do.