Being that I'm the one who started you on this journey of self-doubt, it's about time I put in my 2 cents worth. Firstly, her father technically should be enough of a chaperon for Lavinia heading to a house party. However, my problem was that Lavinia was visiting the house of a single gentleman (2 single gentlemen, if one were to count Cedric). Much like visiting the rooms of a man, this is a major no-no in Regency novels (and I'm guessing the time period).
In Pride & Prejudice, Jane doesn't go visit Mr. Bingley; she goes to visit his *sisters* for lunch. Jane doesn't pay on Mr. Bingley while she's in London, but on his sister Miss Bingley (in hopes that Mr. Bingley is also there).
So, whether Lavinia has or doesn't have her tante isn't really at issue. What's at issue is that there needs to be some woman at the Earl's house for whom society can assume Lavinia and her father as visiting. If the Earl had a daughter for Lavinia to visit, and then he woo'd her (Lavinia, not his own daughter) during her visit with the daughter. However, if Lucius was a widower and had a daughter, Cedric might have someone at the household he could talk to other than the servants. Another option would be if Lucius had a spinster sister (and aunt to Cedric) who clearly couldn't inherit (being that lands cannot be entailed to a woman back then and for VERY much time afterward...). If you added in Cedric's spinster aunt or even the old Earl's dotty widow, the character need not change the plot of the story much. She's only interested in her garden or playing cards with the vicar or something ridiculous as that. She can get up late and go to bed early and take many naps in the afternoon, and basically be almost as absent in Cedric's life as if she weren't really there.
If she were the old Earl's widow, perhaps Cedric's father (or was it his mother?) and Lucius had different mothers, which could account for Lucius disliking his nephew so much, because he had disliked this usurper coming in and taking the place of his mother and bearing a child, so that Lucius was no longer the only child.
I guess you could add in an aunt for Lavinia to act as chaperon since there isn't another gentlewoman at the manor. It would be that Lavinia's father was the one who was invited, and Lavinia would be the afterthought... tagging along. In that case, then YES Lavinia would need a chaperon (more so than just a maid) with whom she could converse and spend the day with while the men were off enjoying their time together discussing things that would bore women (or as so society thought at the time). That chaperon could be her aunt. Men and women in Regency times usually did not spend much of the day together. During the day, women took walks, did needlepoint, read, played the piano, sang, took dance lessons, visited the sick, made calls (visits), wrote letters, and possibly painted, while men had discussions, did sport, went riding (more often than women), thought in their library, toured the estate, made visits (woo'd young ladies), held meetings with their steward (which is what Cedric basically is) making sure that they weren't spending too much money while making as much as possible. Women and met saw each other at breakfast and dinner and possibly (rarely) at lunch or tea. Hence the need for the chaperon, so Lavinia wasn't left to her own devices for too long and get bored and start to flirt with a footman or something otherwise scandalous.
As you said, adding in Lavinia's aunt adds more problems (plot wise), which is why I suggested that Cedric have the spacey aunt instead.
