Hi

(2) is good

(1) is good too. But here, "either" is used slightly differently: to clarify the speaker's meaning and it may sometimes be optional..

- Their two answers are hardly compatible. It means one of them is lying

- You mean Sam is lying?

- I mean either one of them is lying

Hope this helps, Dave

kook jTheir two answers are hardly compatible. It means either one of them is lying.

This is wrong. Here is the correct wording: Their two answers are hardly compatible. It means one of them is lying. "either one" in this context doesn't make sense.
You could say: Their two answers are

Thank you two. I slightly cahanged my sentense 1. Does this work?

Their two answers are hardly compatible. It seems either one of them is lying.

kook jThank you both. I slightly cahanged my sentence. Does this work?

Their two answers are hardly compatible. It seems like either of them is lying.

Regards

kook jDoes this work? Their two answers are hardly compatible. It seems either one of them is lying.

No.

Hi

That isn't quite it. The point is that you should not use "either" in the sentence except in the case where you honestly don't know who is lying and you want to make that clear

You put it quite well in your sentence (2) when you use the word "whichever". This means: I definitiely don't have a view one way or the other (red or blue - say - whichever)

We are interview

Thank you. I first thought my sentense 1's either will perform in the same way below does.

So while I was lying on the beach enjoying the scorching Mediterranean sun and a good friend of mine started talking about ‘planking’, I thought that either one of us (I felt more comfortable thinking that it wasn’t me) had been in the sun for way too long!!

Yes, that all looks OK

The point you make about one / either / any is interesting - it is a rare case in English where there are different adjectives for one / two / many

Best regards, Dave