Quiz on "... or ..."

I am holding out to you my two closed fists. Let us suppose that I know that you know that I know which, if any, of my fists are empty and which are full (for simplicity, I take "full" to be the denial of "empty"). You don't know which, if any, of my fists are empty and which are full. In which of the following cases would I be telling you a lie if I said: "My left hand is full or my right hand is full" while competently using English? (Choose "depends" if you think the answer depends on factors that I didn't include in the description of the case.)

1. In fact my left hand is full and my right hand is full: lie not a lie depends don't know
2. In fact my left hand is empty and my right hand is full: lie not a lie depends don't know
3. In fact my left hand is full and my right hand is empty: lie not a lie depends don't know
4. In fact my left hand is empty and my right hand is empty: lie not a lie depends don't know