@cassandra827
I stand by my reasoning about her not knowing Baek. We know more about him than she does because we've seen a few snippets involving him that she wasn't present for. But just for fun, we don't know him either. What is his story before his adoption? Why is he selfless? How did he end up the clan's leader at such a young age? What are his other characteristics besides selflessness?
Even though he's gotten twice the amount of screentime Baek Han has had thus far we don't know much about Dowun either. What kind of childhood did he have before meeting Lyon? What was he doing while she was away? What kind of shady business did he and his father partake in to get her to the throne? Why does he want power this badly? Why is he so adamant about having a loveless marriage? Does he actually like Lyon or is he repressing his feelings?
All we know about him is that he is extremely smart and emotionally unavailable. I'm sure he's never shared his reasons with Lyon either.
Putting their love life aside, there are other hurdles in their relationship, like the power imbalance. She's very dissatisfied with the fact that she's the queen, but her subjects think his orders are above hers, not to mention all the decisions he makes without consulting her beforehand.
Also, loveless or not, I can't see their relationship working because they lack trust in each other. She knows he's hiding things from her and probably thinks he'll get rid of her the moment she stops being useful, and he... well, he doesn't trust anyone.
The thing with Baek Han is Dowun's own fault for not understanding Lyon fully. He apparently projected and thought she would become a carbon copy of him, but ultimately power and recognition weren't enough for her. I'm not gonna deny she wanted those (after all, getting bothered that people would sooner follow Dowun's orders rather than hers is proof of that), but she also wanted someone to care for her without ulterior motives.
Putting the love triangle aside once more, I think the story's given enough hints that Baek Han is essential for her survival as well. You could argue that she's got other bodyguards, but the author made it so that his fighting skills are unparalleled. Besides, he'd take a bullet for her, which I doubt the other bodyguards would do, especially the one that has the hots for Dowun lol
I'd say she needs both Baek Han and Dowun to guarantee her survival, because they're the best at what they do.