Knowing there's no way out except to runaway (something she doesn't even consider) Lavinia goes along with it, knowing that arranged marriages aren't always awful. Sure, her parents had been... but there are stories of those that ended with love.
And she could technically say no. Neither the Royal Governor Sanford Arlen, or his heir, Tarquinn, want an unwilling bride. But Lavinia isn't certain she wants to say no — it would get her away from her father, a safe and stable life, and is it really that awful being husband to a man who promises to never do more than you want?