This thread is longer than the other one, so I'll reply to this one, although it's interesting both topic titles refer to a "love interest" which makes the other person the object of Hawkman's interest. I would not have put it that way.
With the Egyptians, they both love each other and it's that love and spiritual connection that survives through all their lives. They are each other's soul mate. It's not a matter of Carter Hall having an interest in Shiera Sanders--they are destined to be together. It's like they really have no choice--something bigger than them keeps throwing them together.
With original Katar Hol and Shayera Thal, they are already married when we first meet them. When they use the Asorbascon it's almost a mystical experience as they both access the world memory together. They are one of those couples from Gardner Fox who are happily married and no one else can separate them. Mavis Trent has an interest in Carter (Katar) but he merely tolerates her and Shiera (Shayera) is simply amused. Their marriage is solid as a rock.
It's really only the Hawkworld retcon of Katar and Shayera where it's uncertain if they really want to be together romantically. That's the one situation where Katar could be said to have a love interest in his partner--and same goes for Shayera.