They will not have romantic relation.
In fact you can question if Myne ever have a proper romantic relation with anyone (besides a certain you know who that everyone just say "yup, you're definitely in love with him", EVEN LUTZ)
Because to her, it's not love unless she literally goes dokidoki like in the books.
With that said, Lutz is one of her exclusive specialists that work in creating and distributing books, so he'll work with her, just not a romantic partner.
And the promise of him being her main distribution channel of her products still apply.