When I was younger I might have been more forgiving, but having recently come out of a long-distance relationship of several years with someone who I found out had been lying to me and other people about a lot of things, now I would get out of the relationship and stay well away. If he's been lying about several things even after you asked him to stop doing it, he clearly isn't someone you can trust and doesn't appear to care that much about your feelings. It's admirable that you don't want to "throw the relationship away", but I think you're being naive (in the nicest way possible) if you think that it's worth "saving" a relationship with somebody like that. I doubt he'll ever change if he lies about lots of things. You're better off with out him, however difficult you may find it to break it off. And in my book, even if you personally don't mind it, the drug-taking is bad enough on its own, with or without the lies. If a person has a desire to indulge in risky - and illegal - behaviour like that, then that tells you something about their personality that you shouldn't ignore. I know you probably think you're being open-minded and that open-mindedness is a good thing, but in some cases it isn't, as I have learned to my cost.
Not that it's necessarily important, but: have the two of you never thought about living together? And if not, why not?