Our 13-year-old lies about everything to get what he wants. He lies about not having homework when he does. He hides bad homework from us. We talk to the teachers every day now. He continues to lie even though he knows he is going to get caught. We must search his backpack every night. It seems as if he is constantly grounded from everything. And when he starts to do better and we let him earn back a privilege, it turns out he got away with another lie for a day, or he ends up doing something to remove his privileges again. His answer to us when we ask him why is "I don't know."
I have heard parents complain on numerous occasions about how their teenager has suddenly become a frequent liar I suspect the lies haven't just started; the child has probably been lying for quite a while. What has changed is the parents' awareness of the lies. Now that the child is reaching their teenage years, it is difficult to overlook the lies and it is hard to avoid seeing what those lies are going to do to the child when he reaches adulthood.
In order to deal with lying, you need to understand why your son lies. You have pointed out in your question a very common cause. Your son has determined that the consequences of lying are less than his perceived benefits gained from the lies. I suspect he has told so many lies, he is now in the habit of telling a lie. To break him of this habit is going to take work on your part. It has been years building up to this point, so don't expect it to disappear tomorrow. To stop the lying, you are going to have to upset his perceived benefits. You will have to make it clear to him that telling a lie is going to cost him more damage than admitting the truth. One of the worse quotes I heard was one by Leonard Saxe who said, "If we punish children too harshly for lying, we may make it more likely that they will lie in the future to escape further punishment." The idea is absurd! Does punishing a child for stealing make him grow into a thief? Does punishing a child for rebelling make him grow into an anarchist?
It is not the harshness of punishment that can increase lying, it is our own inconsistencies in delivering consequences. Let's face it: lies are hard to catch. But when bad behavior is not consistently punished, then the child develops the gambling spirit. "Perhaps I won't get caught this time. It will be worth it if I manage to get away with it." Recall that the writer of Proverbs said, "Train up a child in the way he should go, and when he is old he will not depart from it" (Proverbs 22:6). A primary facet of any training is consistent application. It is the only way good habits can be established.
Under the Mosaical Law, judges were given a unique way of dealing with witnesses who lied. "And the judges shall make careful inquiry, and indeed, if the witness is a false witness, who has testified falsely against his brother, then you shall do to him as he thought to have done to his brother; so you shall put away the evil from among you. And those who remain shall hear and fear, and hereafter they shall not again commit such evil among you" (Deuteronomy 19:18-20). A liar in court does so because he sees a benefit to himself -- his enemy is punished. What God did was make the consequence of lying highly painful. Imagine a man lying, saying that Billy caused Jack to break his leg. The court delivered punishment for injuring a fellow man was for the same injury to be done to the perpetrator. A liar in such a case would receive the punishment the innocent man would have received if the lie had been believed. Harsh, but it makes lies a serious matter.
Let us use this as a method of dealing with your son's lies. First, notice that the judges did not accept everything the witness said. They were required to make a thorough investigation. In your case, you know your son lies about the homework he is required to do. Hence, we tell him that since he has proven himself to be untrustworthy, you will be checking everything dealing with homework until he has proven his return to truthfulness. You are doing the first steps: checking what he brings home and talking with his teachers. The schools here post the days' assignments on the Internet allowing parents to check day or night what the student was expected to do. Since he has not been truthful, do not accept any excuse of "Oh, I did that during study hall." Either he brings the completed work home to show you or a note from the instructor saying the work was turned in. Any lack of evidence is his problem. He started it by lying, so he is going to have to redeem himself by providing evidence.
Now, what is to be done if there is incomplete work or lack of evidence of completed work? He is required to do it first before he can do anything that he desires: no playing, no visiting, no phone, no radio, etc. This should be the rule even for assignments that are not due until a future date. You might as well discourage procrastination while you are at it. What happens if he forgot to bring his textbook home or some important piece needed to get the work done? Then he spends the remainder of the day in his room. And, by the way, his room should be stripped of everything but the bare essentials while he is on "probation."
You are probably thinking, "Easy for you to say all this. He is going to throw a fit!" This is where Dad steps in. If your son insists on acting like a child, treat him as a child and give him a spanking. There does not need to be any anger in its delivery or a desire for vengeance. It is a matter of delivering the consequences to his chosen actions. "Foolishness is bound up in the heart of a child; the rod of correction will drive it far from him" (Proverbs 22:15). Yes, I sure you are going to be in for several rough weeks or even months, but remember you are trying to undo bad habits instilled over a long period of time. It is going to require diligent effort on your part to not only break the bad habits but to also instill good habits in their place.
Notice that the lies about homework were not punished directly. I did not have you punish each caught lie individually. Rather I had you focus on what he hoped to get away with: avoiding doing the homework or at least gaining a delay so he could do other things. The reason for this is simple. It is hard to catch every single lie. Instead, we assume that one lie indicates others exist. If he gives you the line, "Don't you trust me?" The answer is "No." What we do is put the consequences squarely on his own shoulders. He has to prove himself trustworthy and only time will tell. How much time? Since this is an ongoing problem, I would make it for no less than two months but preferably for an entire school year.
A child who lies about one thing is likely to lie about other things. As you discover lies, handle them in a similar manner. Look for what he had hoped to gain from the lie and then remove it for a significant period of time. Require him to provide evidence that makes it near impossible to continue to lie about that matter. Make the matter clear that trust will not be restored until he shows consistent good behavior.
Keep in mind that only by consistent application are you going break him of his habitual lies. If you give in just once, you will set yourself back for weeks of progress.