I guess lying is one option, believing a liar is another option, and... well, are there any realistic options beyond that?
Sure. There is a very popular option of "I will look only here, I will not look there and even if I accidentally glance over there, I will quickly avert my gaze and feel guilty about my transgression".
Deliberate ignorance combined with cherry-picking evidence can get you very very far.
But how do I distinguish between these two options, in real time?
If only there were some way to think about the two options in something like probabilities... :-)
I tried communicating with mindkilled people in the past, it didn't go well.
You mean to tried to deconvert them? No surprise it didn't go well.
Note that the aims of the conversation can be quite limited, though. It's up to you to define your goals and they don't have to be "convince that person that her belief is wrong".
I've started a podcast called Future Strategist which will focus on decision making and futurism. I have created seven shows so far: interviews of computer scientist Roman Yampolskiy, LW contributor Gleb Tsipursky, and artist/free speech activist Rachel Haywire, and monologues on game theory and Greek Mythology, the Prisoners' Dilemma, the sunk cost fallacy, and the Map and Territory.
If you enjoy the show and use iTunes I would be grateful if you left a positive review at iTunes. I would also be grateful for any feedback you might have including suggestions for future shows. I'm not used to interviewing people and I know that I need to work on being more articulate in my interviews.