Appendix A Part II of Return of the King states that Eomer wedded Imrahil's daughter Lothiriel on the last day of the Third Age. LOTRO puts a romantic spin on it, with Prince Imrahil wondering why mentioning Eomer made his daughter blush. But it's also possible that this was a political union, further cementing the bond between Gondor and Rohan.
I doubt that Prince Imrahil would object too much about having Eomer as his son-in-law. He has personally witnessed Eomer's valor and knows of his friendship with Aragorn. Lothiriel would also be a queen. Still, Lothiriel is Imrahil's only daughter and youngest child, so he may be a bit protective of her. LOTRO has Lothiriel looking quite uncomfortable during Aragorn and Arwen's wedding feast as her father mentions talks to the player character about Eomer.
So what do you think brought about Eomer and Lothiriel's marriage, love or politics? I will admit I hadn't thought much about this before playing that scene in the MMO, but on reflection, and Tolkien says nothing more apart from Elfwine coming from their union and succeeding Eomer. It seems like a 50-50 chance of either possibility.