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".