I think he only actually lie if Tav romances him, no? about the whole bomb and his ex that he only tells after he slept with Tav. If not in romance I don't see lies, he just says that he won't tell you and demands blind trust. I say demands because he is adamant and if you refuse (which let's be honest makes sense in this case) he will go after other ways to get what he needs.
Even then, he doesn't lie to you.
He tells you his situation, and it's not a good one, and before that he is reticent to tell you about it, but even then, he doens't just keep you completely blind - he tells you what he needs to remain healthy and asks you to trust that he is being honest about the seriousness of this need... And it turns out he is, in fact, being honest about the seriousness of the need. So... what lie?
I don't agree that it makes sense to refuse his request, either... why do you say it does? I've never had any issue giving him what he needs, personally. It's never been a burden to me to do so, and he's a friend that, unlike pretty most of the others, is actually decent to me as a person, so I'm happy to help him out when he asks.
