Work had been piling up for Luca but he didn't want Sophia to know.
The time he was in the hospital with her, he had to take calls from various executives and answer emails constantly. Considering he was on the hot seat for having disappeared for a couple of weeks, he wasn't willing to risk his position further.
Without his position, he couldn't keep tabs on his father. That was the only thing he could offer Miss Marcaida to keep her on his side so he was going to fight to retain it.
Once the war he was about to start was over with, he didn't care about his title all that much. He had nest eggs elsewhere that would give him much money if worse came to worst.