]if she believed Wickham did not love Miss King, would she not have the same judgement on him as she did on Charlotte?

I think we are being shown some of the "prejudices", which Lizzy has to learn to acknowledge in herself. At the end of Volume 2 Ch 3 when Lizzy analyses her feelings about Wickham's defection, she is described as "less clear sighted perhaps in his case than in Charlotte's". The text is directing us to notice the imbalance in her judgement.
So - why does she think this way? I believe she is disappointed in Charlotte, because as a close friend she expects to share the same set of values and standards. Charlotte has been faced with the same "temptation" as Lizzy (OK Mr Collins himself is not very tempting, but in material terms his situation is) and succumbed to it, where Lizzy scorned it. She can justify her revulsion for her friend's act from her own morally sound position.
Wickham, on the other hand, she still has a soft spot for - ie she is prejudiced towards him. She has exercised her reason and not fallen in love with him, because neither has any money to marry on; she merely takes the arguement one step further and allows that he has to marry someone with money. She tells her aunt that she cannot find she is "in the least unwilling to think her a very good sort of a girl" - not a bad partner for Wickham, then - but she despises Mr Collins as unworthy of any sensible woman.