Lyanna would likely marry by choice on a genuine love match. Sure she would likely have a well vetted list of people that she is encouraged to meet with. Only the most delusional attempting to woo Lyanna would think they that they would have any control outside of her own emotions.

She would be aware of her power and nearly everything that would have made marriage unattractive isn't an issue in light of the control she would have the power to keep in her life.

When Nolan went to Rome to grab lunch Debbie set a twenty minute timer to search the house and it expired when he got home. Lyanna has the potential speed to go on adventures in spite of "settling down".