That would be the unambiguous way of saying it in Swedish, but as I stated in an earlier comment on this page (look for where I say "I dislike this sentence"), this sentence can be interpreted that way too. So it's an accepted answer.
PS It's better and clearer to say it with skulle, but just hade is used too, especially colloquially.
No, in english, this sentence would just make more sense being said, I have not lived without you. It doesn't make sense past tense, because how can you not live up to a point, then be alive again, as in this sentence presuming whoever is saying this is alive.
Edit: I meant have, not had has, sorry.
I see. That would be Jag har inte levt utan dig in Swedish. You'd use the other sentence in contexts like this: I was only 17 years old. I had not lived without you (yet) and I didn't know how to deal with … whatever
I dislike this sentence for another reason: it's ambiguous in Swedish. It can mean either the situation I just described, or it can be interpreted as I wouldn't have been alive now if it hadn't been for you.
This is not the past participle, but the supine form, used to create the past perfect (pluperfect) and the perfect. The trusty SAOL says that levat is an alternative form for the supine, but it does not list any alternative to the past participle, which is also levt.
I think levat is more colloquial but it should work here too, I'm adding it as an accepted answer now.