yes you can lie on the MMPI or any other test just like you can tell a lie to your parents or whoever you dont want to know the truth.

The MMPI is like taking the SAT's in school. its a paper with questions on it and a bunch of squares or circles for yes, no, never always and sometimes. you read the question and you color in your answer.

Are you thinking about killing your self yes no sometimes or always. I can choose to color in any of those choices. I can color in the circle for no if I dont want them to know I sometimes think about suicide.

it is true that the MMPI has a lie detector. those are questions that are validity questions where according to my psych classes are questions that are worded in a way that the answer is supposed to be a yes or no, but when people are trying to lie on the test these questions end up being marked always or never and they are never the same answer when same question is asked multiple times.