Since, as Stephanie points out, nothing in the text points to Lucy's scheming for a meeting, Austen may well have not intended us to interpret the meeting as a planned one. However, the timing of it and the fact that Lucy is such a schemer and JA points out over and over Lucy's natural cleverness, her shrewdness and her sharp eyes, I feel that gives us enough leeway to also consider that Lucy did scheme and was fortunate enough to have it work.

First of all, my Norton Critical text footnotes the word 'discovering' as meaning 'disclosing.' I checked Johnson's and the first definition for 'discover' is 'disclose.' I interpret this as indicating that Mrs. Jennings and the Misses Steels knew each other already though the relationship is probably not an intimate one. Lady Middleton has likely never seen them because she obviously abhors and keeps far away from relatives and friends of her mother because they represent trade, non-gentry and folks of the lesser professions. That is why she is upset when she hears about Sir John's invitation to Anne and Lucy. She expects they will be unfashionable and lacking in manners and so on. Her mother, on the other hand, generally likes to keep up with people not caring the least bit about appearances.

Edward is Lucy's ticket out of the 'poorhouse' and I'm sure alarm bells went-a clanging all over the place every time Elinor's name was brought up and once Edward left (heading for Barton Park, no less), the wheels started spinning on what she could do to make sure she didn't lose her bankroll after already giving up four years and she came up with: let's get to Exeter and hope something happens. True there would be no guarantee that they would run into the family but Lucy would know this beforehand and be clever enough to lessen the odds as much as humanly possible without having to hang around waiting everyday, something she would certainly not want to be seen doing. But Barton Park is only four miles outside of Exeter so it would be well known amongst the populous---the everyday working folk as well as the gentry---as would all the large estates within a reasonable range. Not only that, Sir John and Mrs. Jennings, as such gregarious, outgoing and friendly people, would easily make noticeable any patterns of excursions and places they visited with regularity. We've seen Lucy at work. During this time period the admiration, discussion and visitation of estates was popular. It would be easy for Lucy to start up a conversation with a clerk, etc. about Barton Park and segueing to its inhabitants while purchasing ribbon or something and discover enough to make the playing field even for a hoped-for meeting, fifty-fifty if not better.

Not only that, I'm sure Lucy would be smart enough to make herself familiar with Sir John's crest. The Steeles wouldn't even have to see the Middletons literally, but be able to recognize the crest on the carriage waiting outside a shop or whatever.

A reader could go either way on how they feel about this. For my part, it's hard to see the ever clever, ever skillful, spiteful Lucy sit back and just opine that what will be will be without giving it her best shot. If that hadn't worked I could see her trying to come up with the next best thing. :)