]Lucy’s efforts to discover Elinor’s feelings and true relationship with Edward smacks of desperation

I agree, Lucy's desperation really comes through in several of her speeches. As sly as she is, her motives and jealousy are quite obvious. When she mentions Edward's being "cast down" while he was visiting them at Longstaple, it's pretty obvious that Edward isn't cast down because he cannot marry Lucy yet, but because he has to marry her at all!

...poor Edward is so cast down about it! Did not you think him dreadful low-spirited when he was at Barton? He was so miserable when he left us at Longstaple, to go to you, that I was afraid you would think him quite ill" (ch. 22).

"...it made him so melancholy, not being able to stay more than a fortnight with us, and seeing me so much affected" (ch. 22)

"Edward's love for me," said Lucy, "has been pretty well put to the test, by our long, very long absence since we were first engaged, and it has stood the trial so well, that I should be unpardonable to doubt it now. I can safely say that he has never gave me one moment's alarm on that account from the first" (ch. 24).

"I am rather of a jealous temper, too, by nature, and from our different situations in life, from his being so much more in the world than me, and our continual separation, I was enough inclined for suspicion, to have found out the truth in an instant, if there had been the slightest alteration in his behaviour to me when we met, or any lowness of spirits that I could not account for, or if he had talked more of one lady than another, or seemed in any respect less happy at Longstaple than he used to be. I do not mean to say that I am particularly observant or quick-sighted in general, but in such a case I am sure I could not be deceived" (ch. 24)