If everything you say is a lie, then the statements ‘everything you say is a lie’, and ‘you always tell the truth’ are both lies. Which means the first statement could be that some things you say are lies and you always tell the truth is one of those lies.
Also if the genie is a thinking agent or even just capable of detecting an infinite loop this falls apart.
Imagine trying to ward off a genie by yelling: “THIS STATEMENT IS FALSE!”
EVERYTHING I SAY IS A LIE, I ALWAYS TELL THE TRUTH!
instant
If everything you say is a lie, then the statements ‘everything you say is a lie’, and ‘you always tell the truth’ are both lies. Which means the first statement could be that some things you say are lies and you always tell the truth is one of those lies.
You are now stuck in an infinite loop with a rabbit and turtle.