Lysimachus is the Governor of Mytilene, and not unknown to the brothels, though he is cautious and insists that the prostitutes he takes are disease-free.
He is kind to the women he pays for there, and affected enough to not want to admit to what the trade they ply is. Like all the other men exposed to Marina, he is quickly converted from his lecherous ways and is very generous to her for it. He is intrigued when a ship decked in mourning approached his port and goes out to meet it. His opinion of Marina is by this time high enough that he agrees she may be able to cure the catatonic Pericles. Apparently he never tells Pericles that he first met Marina in a brothel, as he is able to convince the Prince of Tyre to let him marry his daughter.