These lies are so ridiculous, no one could believe them, and IMO Jodi knows this -- nevertheless, she will never give the family or Juan the satisfaction of telling the truth about anything.
She is not legitimately trying to defend herself on the murder charges. She knows she's at least going to spend her life in prison, and she has come to terms with that IMO. The only reason she is putting on a defense at all, and self defense in particular, is to allow her to hold forth about her relationship with Travis and to tarnish his legacy because she is still pissed at him.