I think for Ms. Lance case, her family and friends have been pushing the idea of Mr. Dalton having feelings for her and due to his status, I dont think her family would be opposed to the idea of him proposing. They keep putting the idea and exaggerating the conversations and moments they share to be something more. And since theres rumors apreading about them being close and since he is inviting people over to the manor, it adds more to the idea. Also, I think for some nobles, they would make a public announcement of both parties are on the same terms and then work together after said announcement. Or, maybe asked the family through letter and received an unofficial blessing but it being enough to make engagement speech.
That's my take on it, I dont know too much but hopefully it helps, or if someone else can explain and add to it!
So quick question for those who know about the intricacies of nobles. Why does the blonde think the proposal is for her? Wouldn't she be aware? I ask because isn't it common practice for the groom to ask for the brides hand in marriage from her father before the proposal even happens ?? And her family isn't even there.