Hello. You describe your boyfriend as “lapse Jehovah’s Witness”. You haven't said if he was baptized or not. If he was baptized that would be a reason why he doesn't want to take you to the Kingdom Hall with him since he could end up with elders starting to question him as to his relationship with you. If he has been sleeping with you, this would mean he would have to either break off relationship with you or be disfellowshipped and since he's trying to get back in, it would be a big hussle for him to get disfellowshipped and return since he would still need to break any ties with you or marry you.
If he wasn't baprized I don't understand why he wouldn't take you with him since he has nothing to lose other than some gossip by others but that's nothing.
Either way, if he slowly drifted away from watch tower religion because it was too strict too follow, he obviously still believed that their teachings were all true and that this religion was and is the truth and that is why he may say that he's not worthy of being called Jehovah's Witness. That is his guilt conscience telling him that he is deserving death as per Watch Tower doctrine and this may be why he wants to return to the cult. Obviously people within a cult don't realize they are in one and neither does he nor did many of us here realize it.
It depends on his power of reason and is he honest to examine facts or is he just a nice person but not a deep thinker if you get my drift. Since you have very little knowledge about wts it may be hard for you to reason with him on doctrine so try to research one topic and stick with that topic until he at least sees that what you're saying is correct. The main dogma of wts is that Jesus returned in 1874 1914 :) Do some research and discuss it with him. He may not feel strong in the faith and that is why he may try to have you talk to someone else but don't worry the others won't know about wts' history and it's details because that's the who deception. Their only answer could be that what you bring up is old history or "old light" and doesn't apply today which is not logical if they were led by God's Spirit as they claim. Use ONLY wts publications to show what they taught, since many times they make it appear that in early student thought that Jesus returned in 1874 (I'll use Christ's return as example for your discussion). But it wasn't until 1943 that 1914 because "truth" of Christ's return. So they taught public for some 50 years that Jesus returned invisibly in 1874 and not 1914 and since they claim that Jesus appointed them in 1919 them teaching 1874 after that date doesn't make any sense. I always recomment reading Charles Russell's book Thy Kingdom Come on seeing what was originally taught by wts. Stick with one topic at a time so there is no way of skipping what is being discussed and letting him or any JW going on the offensive and trying to change topic to point out your religon's shortcomings.
If you need specific answers or help or obtaining PDFs of old publications just ask.