I've always found the conversation in Ch. 24 just icky. That must say more about me than what goes on there. It's interesting that Elbe used sports analogies.

In Ch. 23
Elinor
wanted to hear many particulars of their engagement repeated again, ...
whether there were any sincerity in her declaration of tender regard for him...
she particularly wanted to convince Lucy, ... that she was no otherwise interested in it than as a friend...
she could not deny herself the comfort of endeavouring to convince Lucy that her heart was unwounded.

These were Elinor's aims going in and perhaps the most laudable to me was to find out whether Lucy truly cared about Edward.

So brave Elinor engages Lucy and her "little sharp eyes full of meaning". Doesn't that description tell us everything we need to know about Lucy?

Lucy went on. "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."

"All this," thought Elinor, "is very pretty; but it can impose upon neither of us."

I'm not sure what Elinor is thinking here. Is it just that they both know that what Lucy just said is exactly what did happen?
They both seem to know what the other is about and Elinor is the victor perhaps because she's pointing out the truth of the bad state of Lucy's situation, in a secret engagement likely to drag on forever.

After I read your response TomP2, I tried to figure out why I find this conversation so distasteful. I loved when Elinor gave Marianne and Willoughby a verbal smackdown when they were disrespecting Col. Brandon. Maybe it's because she cared about them and there was the hope they might see the error of their ways. With Lucy, the smackdown will make no change in her. Indeed, it didn't even stop her from trying to enter the subject again and again.

At the end of the conversation, this quote always gets me,
Lucy: If you could be supposed to be biassed in any respect by your own feelings, your opinion would not be worth having."

Elinor thought it wisest to make no answer to this, lest they might provoke each other to an unsuitable increase of ease and unreserve;
Ease and unreserve seem to be positive words, but in this situation they are not. I think it means, if they start speaking very plainly, instead of the veiled manner they had been, slapping and hair pulling might ensue. :-)