While we try to keep a universal front with his mom on discipline, her interpretations of what he does right and wrong differ from ours. Mostly, she has high expectations of him that he never meets. I think that my stepson is exactly like my husband in every way. I also think that my husband and my stepson have ADD and overactive appetites. My husband is a kind and wonderful person and I only hope my stepson will grow up to be one, too. What can I do to help, especially about the lying?
You say that you and his father keep a united front on discipline. That's very good, but it should be discipline for when he is at your home on the holidays. I encourage both you and your husband to not discipline your stepson for things he does while at his mom's home. Avoid grilling him and chastising him by saying things like "Your mother said that you.." Instead, have conversations with him about how it's going without taking his side or hers. You can explore ways that he can interact with his mom that might make things better. Avoid putting him or yourself in the middle. The lying, being overactive, and constant eating might be due to anxiety that he feels at his mom's home, but you can't do anything about what happens there.
You can, however, create a safe place in your own home where your stepson can be happy during the holidays, and help him deal with what goes on at home. Both homes don't have to have exactly the same rules. Your stepson is old enough to understand that what is permitted in one home is not necessarily so in another -- he has to adapt to where he is.
Your husband might suggest to your stepson's mother that she enroll him in a divorce group at school where he can learn positive ways of dealing with the divorce and where he can share his feelings with others. Kids of divorce don't want to hurt either parent by anything they say, so they need a place to vent. A divorce group could do just that.