@Kurii The conversation didn't flow that way. But you know the king and queen know. It's probably the only reason they were willing to allow the engagement at all.
But if the former crown prince dies on crusade, then Lucia is an engagement-widow. (Yes, there's such a thing. Unsurprisingly, it SUCKS for the woman.) Unless she's ordered to stay at the monastery or convent, she could find another husband. Theoretically.
And if Lucia got pregnant by that one-night stand (a good reason for the royals to want to keep track of her), it's extremely unlikely that Lucia will ever see the child. The royals will take the kid once they're born, and either farm them out to a trusted minor noble, or adopt them into the royal family proper, but with no right of inheritance to the throne and most of the royal-associated titles and land.