I don’t think any sort of friendship can be happy by chance because even between the best of friends there will inevitably be differences to tolerate if you wish to continue together and Lizzy & Charlotte have come upon one. Marriage has the potential to strain previous friendships or just pull them apart, at least this has been my experience, but Charlotte foresaw more, that Lizzy would not understand her choice and worried her reaction would affect their friendship:

The least agreeable circumstance in the business was the surprise it must occasion to Elizabeth Bennet, whose friendship she [Charlotte] valued beyond that of any other person. Elizabeth would wonder, and probably would blame her; (Ch. 22)

However I am not sure if Charlotte truly understood how much Lizzy sees her choice exposing a disconcerting difference of principle or how much she has sunk in Lizzy’s esteem:

She [Lizzy] had always felt that Charlotte's opinion of matrimony was not exactly like her own, but she could not have supposed it possible that, when called into action, she would have sacrificed every better feeling to worldly advantage. (Ch. 22)

Charlotte’s choice makes a difference in the relationship immediately so she was correct to worry:

Between Elizabeth and Charlotte there was a restraint which kept them mutually silent on the subject; and Elizabeth felt persuaded that no real confidence could ever subsist between them again. Her disappointment in Charlotte made her turn with fonder regard to her sister, of whose rectitude and delicacy she was sure her opinion could never be shaken… (Ch. 23)

It is a testament to their pre-engagement friendship that both ladies want to keep the other in her life. Charlotte takes steps to assure it in Ch. 26. At her farewell visit she secures Lizzy’s correspondence: “I shall depend on hearing from you very often, Eliza” and a promise to visit her at Hunsford. Lizzy wishes to keep the friendship alive as well. She was “sincerely affected” at Charlotte’s leaving despite the disappointment her choice had raised. Lizzy readily assures Charlotte of frequent letters but has to be persuaded to the visit. She first responds with “We shall often meet, I hope, in Hertfordshire” as she “foresaw little pleasure in the visit” and I can’t say boo to her reluctance at spending time with Mr. Collins. Lizzy agrees to the visit but I think simply for Charlotte’s sake.

Charlotte was concerned about their friendship when she first accepted Mr. Collins but I am not sure she is still troubled during the Hunsford chapters we have read so far. I am kind of troubled. I think Charlotte’s “opinion it admitted not of a doubt, that all her friend's dislike would vanish, if she could suppose him to be in her power (Ch. 32) shows, as Kathleen (elder) pointed out in post 44589, that Charlotte does not really understand Lizzy’s ideas on men and marriage. If Charlotte is still so misled to think Lizzy would accept Darcy just because he likes her it seems she has still not understood how much Lizzy’s opinion of her took a beating either.