at this point, all we know for certain is that EG experimented with meth (
http://www.kansas.com/news/local/crime/article208704089.html) and while some of the photos are damning, we dont know if her active use overlaps w Lucas' disappearance. that being said, she had experimented with it and i have a very, very hard time believing JH didnt know.
-do we we know how long he has been at his job? this could have been something JH experimented with when he and EG first met or even earlier in life and then stopped later bc of the job and/or other reasons. i do find it hard to believe two people are living together (even violently) and one does hard drugs and the other does not. if its something they shared at one point, it could explain why he was OK continuing in a relationship with her.
-or alternatively, if hard drugs really isnt JHs thing, it could be something EG tried when he wasnt around. HOWEVER, i dont believe he didnt know, even if he is gone a lot. you eventually learn these things about your partner - whether they confide in you, tell you the partial truth, stumble upon the info from living together. in this instance, it was also part of the boys' father's custody battle. Somehow, JH would know that EG did/had done hard drugs, imo.
so, in my mind, i cant paint of a picture of a dad, even one who travels a lot, who both doesnt know his child is being abused and his partner is doing/has done hard drugs. at the beginning of this case, i maybe would have given JH the benefit of the doubt on being blind to one of those things but now, its too many things. while i dont think he has any clue what happened to Lucas, he may hold the key to the answers bc he knows more than he realizes by living with EG. but getting him to come around to that logic and realize the environment he left Lucas in is probably a huge battle on its own.