] I try to imagine a parallel situation where a similar incident which happened to Jane happens to Caroline instead. I can't say that I would be entirely positive that Lizzy would feel the same in Caroline's situation because her emotions are not engaged in the same way as they are with her dear sister.

I think one would naturally have more sympathy over the heartache of a beloved sister than an acquaintance, even when it's an acquaintance one likes. On the other hand, if Caroline had her heart genuinely broken due to someone else's prejudice against the daughter of a tradesman and/or due to misinformation, I think Lizzy, as a generally compassionate person, would have had some sympathy, even for Caroline.