Before I begin, I should say a few things. The house I built in Hearthfire is Lakeview Manor. I have adopted Alesan and Lucia. I am married to Camilla Valerius. The problem I am having is that whenever I walk into Lakeview Manor, Lucia is constantly following me around; and everytime she gets close, speech options start popping up. Alesan is fine, however. is there any way to fix this, so she can stop bugging me?

don't ignore her. If she wants to do something and you indicate "not now I'm busy" she will keep asking. Indulge her, she is your daughter after all. Play a game or something with her. She should stop getting you into a conversation. I have encountered this before. Ended up playing hide and seek with Sofia and she didn't ask me again for anything for several days.