How to make a program that lies one-third of the time?
The concept you have going is 'OK' (cumbersome, but for a beginner it's OK). There are two bugs, and one recommendation that will help a lot.

First the recommendation....

Change numLies to be a boolean value like: boolean canlie = true;

Then, your code becomes:

if(canlie &amp;&amp; itsLieNum == 1){
    canlie = false;
    ....
} else {
    canlie = true;


This makes the purpose of the code more apparent. Also, a bug is that you have to declare this ourside your method. It should be a class-variable, not a method variable, otherwise it will always be the wrong value.

The bug you have is a technical one (but important that you learn) ... Random.nextInt(value) will never return the input value. It will retrun 0(inclusive) to value(exclusive). In your case, with nextInt(2) it will only ever return 0, or 1. Change that to be nextInt(3) and you will get the values 0, 1, or 2 and it will be 1 1 third of the time.