Yes indeed. I can't see how Lucy coudl have possibly "manipulated" in this way. Even if she had heard of Sir J etc, it would not be that easy to get to see him.

She and Anne woudl have had to keep goign to Exeter repeatedly, hanging around such places where "teh Quality" went, to try and scrape acquaintance with them. I dont think that there woudl have been that many places and it would look odd and cost more money than they could spare, Im sure, to be staying at an inn where Sir John might stay the night or go for a meal.. and it would look odd for 2 ladies to be behaving like that. Or hanging around fashionable shops.
I think it is far more plausible that it is meant to be a lucky chance that she met Mrs J, and possibly managed to find some common acquaintance or a distant cousinship... which allowed her to put herself forward for an invite. Just becuase she's a sly selfish woman does not mean that she's super prescient....