Finally. She found her life in USA, while no one helped her in Croatia.
That's difficult to assert, without equivocation. Maybe. It always seemed as if the whole situation was complicated on both sides. Croatian tennis federation big-wigs were perhaps understandably ambivalent about her "asylum" situation and how it went down, while Mirjana did not exactly have a lot of trust that officials in Croatian Tennis had her best interests at heart.
The whole affair was a lot to shoulder for a teen girl, long after the initial break. That much pressure (fleeing a homeland, seeking foreign asylum, supporting an entire family) ought never to have been placed on a developing player; it clearly played a part in stunting her career. One suspects there was a lot of miscommunication over the years between the Lucic clan and Croatian tennis powers, and vice versa. Ancient history, now.
The fact is that she identified totally as a Croatian citizen through more than a decade following her request for asylum, even when life was difficult for their family in the USA. It seems highly unlikely that she would change that now. I think ajmo is probably correct. This move is likely logistic, in terms of squaring-away a life that will mostly be lived with her husband in the USA, and also to facilitate travel for a couple more years of tennis. It made a lot of difference for Varvara L, when she finally got her citizenship, but her case was much more difficult.
I would think Lucic will always identify as Croatian, first and foremost, while maintaining the benefits of a duel-citizen status.