That is pretty good :-)
I tried several times as I have been investigating sending some of the "meta" questions to these models. I just tried again and this is what I got:
"If a person says "I am lying," it could mean either that they are telling the truth about the fact that they are lying, or it could be a lie itself. It is important to consider the context in which the statement was made and to try to assess the credibility of the person making the statement. It is also important to remember that people may not always be honest or sincere, and it is always a good idea to verify information before accepting it as true."
I could never make it mention the Liar Paradox. Is that all that you sent?