In my opinion, Elizabeth uses Fi. Here is a quote from a post that argues that she is an ENFP: ''She refuses to marry for anything other than love, but does not share her feelings about Darcy as they shift and change until the last possible moment. Lizzie reacts to a slight against her with mockery, preferring not to talk about it with Jane or Charlotte but to instead divert attention away so she can process it in private. She is appalled that Charlotte would marry someone as irritating as Mr. Collins purely for security. Even though she believes her father is wrong in not stopping Lydia from going to Bath with her friends, she respects his decision and does nothing to impede it. If Lizzie does not like the company in the room, she excuses herself, turns to a book, or makes a polite mockery of them in private. Lizzie has very little regard for status or position and refuses to answer questions from Lady Catherine that she dislikes or to submit to her authority. Even though Lizzie believes in marrying for love, she freely admits with a twinkle in her eye that seeing Pemberley made all the difference in her affections for Mr. Darcy, because, after all, being in love is a fine thing… being in love and a wealthy woman is an even better thing! Even though she is initially outraged at Darcy’s allegations against the behavior of her mother and sisters at the ball, she is detached enough to see that his bias is well founded and factually based (they are inappropriate) and so concedes he is right and his opinions are valid. Lizzie flat out refuses to marry Mr. Collins out of dislike, and minces no words when telling Mr. Darcy all the reasons she would never accept his proposal". Even if you argued that she uses Ni, then I guess she could be an ESFP, or an INTJ (which I think is highly unlikely).
I also think she is an Ne dom-she is very playful and witty (based on my experience ENFPs are much more playful than INFJs). She has a "lively, playful disposition, which delighted in anything ridiculous"...very ENFP. Also, I think that Ni dom would be a better judge of character, they would have intuitvely known that Darcy was internally a good person. Rather, Elizabeth needed more experiences with Darcy to truly make out his character. And just because she likes to analyze different characters doesn't mean that she's an INFJ, most NFs in general enjoy doing this.
So these are my overall opinions:
-Mr. Darcy: IxTJ, I used to think INTJ but honestly I'm not sure anymore.
-Elizabeth Bennet: ENFP
-Charles Bingley: ESFJ
-Mister Collins: ISTJ
-George Wickham: ESTP is a possibilty...what about an unhealthy ENFJ? He could be possibly manipulative due to auxiliary Fe...
-Lady Catherine de Bourgh: ESTJ
-Jane Bennet: I've seen ISFJ, ISFP, and INFP. She is certainly an Fi user, because she has difficulty revealing her emotions to Bingley. But I'm not really sure whether or not she uses Se or Ne...
-Mrs. Bennet: ESFJ
-Lydia Bennet: textbook ESFP
-Mr. Bennet: INTP
-Mary Bennet: ISTJ
-Caroline Bingley: ESTJ
-Georgiana Darcy: Yes, some sort of IxFJ, I think ISFJ
-Kitty Bennet: ISFP (introverted version of Lydia)