We are glad you are reaching out for help with this young man. You mentioned a number of things he is not interested in such as academics and sports. Is there anything that he IS interested in doing? Does he play video games, or does he leave home to go hang with buddies? Do you suspect he might be using substances, smoking pot or taking other drugs? You mentioned the environment at his father's is much different than at your home. How much time does he spend there compared to your home? When he engages in dishonesty and inappropriate behaviors in school, what happens as a result? Does he lose privileges or have extra chores to do? It seems that every misbehavior has a function. The goal for you is to figure that out and help him learn other ways to get those needs met in appropriate ways. For example, when he lies, is he trying to avoid negative consequences? And when that works, is he feeling smarter than the adults in his life? If so, that will reinforce his belief that he is smarter than adults and increase the likelihood he will continue to be dishonest in the future.
When he is disruptive and disrespectful in school, is he choosing those behaviors instead of letting anyone know that he is struggling to understand or to complete the current assignments? Often, we hear of kids doing things like this simply because they don't want their peers to think they CAN'T do the work or are struggling. To put it in “kid" language, they would rather other kids think they are “misbehaved" than to think they are “dumb." It is sad but true.
We don't know what this young man has experienced in his life but currently there are counselors and therapists who focus on areas like trauma-based therapy and approach things a bit differently because of the effect trauma has on the youth's emotional development. Check the internet for counselors and therapists in your area or ask a school counselor, your doctor or a trusted adult for any recommendations they might for a counselor or therapist.
We hope that soon someone will be able to help him. Let us know if we can provide you with additional information or help.