Elizabeth *is* extremely upset, after all, and it might be that if she didn't confide in *somebody*, she would burst! ;-) Also, if any outsider could understand what she was going through, it would be Darcy, and IMO she's convinced she can rely on his discretion. At the moment, Elizabeth has no reason to believe things will turn out well, and soon *everybody* will know what happened. ("It cannot be concealed from any one.") Darcy is only getting the news a bit earlier than most, that's all. It's only in retrospect, when they know that Lydia will be getting married after all, that Elizabeth wishes she hadn't confided in him.
I do agree that telling him about Lydia is a kind of repayment of his trust in her when he told her his sister's story.