Asriel & Coulter's relationship

[Lera]

As for me, MC and LA are the most beautiful and strange pair I've read about. I don't agree with many things they've done, but I can't not to like them. I think, they were too proud to believe in love between them. P.S. sorry for my English.

[tyche]

I think they love each other. Absolutely. It's more clear in TAS than in NL but i think it's pretty evident in all the books (well i guess not in TSK since they never interact).
Mrs Coulter and Lord Asriel are enemies. She works for the church which he despises and she thinks his work is heretical so when they meet on Svalbard both have every reason to kill the other but they don't. Instead they almost team up. I guess you can make a case that Lord Asriel just wanted her help but i really don't buy that. I mean, he doesn't need her help at all, he knows she's the most untrustworthy person ever and he lies about what he's doing so she couldn't be that helpful anyway.
I don't think you can say it was just lust either. Lust isn't strong enough to continue to bring two people who are completley philosophically opposed (considering both feel the other is doing things that would compromise their own souls and salvation) together time and time again for 12 years.

[Lera]

I think their unusual relationships make us to admire them. They loved each other, but at the same time they both loved freedom and their statuses too much to be together.