Catherine spends that night in Henry's room, making love and watching searchlights roam the sky. In the morning, she prepares him for the operation and warns him that the anesthetic tends to make people chatty, so he should be careful not to brag about her.
The searchlights are part of the Milan defenses. Even as they make love, they can't escape the war. And in the daytime, they must hide their relationship entirely.
Catherine then asks Henry how many other women he has loved. He says "None." Next, she asks how many he has slept with. He gives the same answer, though they both know he's lying. Even so, Catherine is pleased at these responses.