At this accidental meeting at Pemberley, both Lizzy and Darcy are surprized, and embarassed. Lizzy certainly expected Darcy to avoid her, and probably Darcy must have felt the same about her.

I think, it took a lot of determination, and humility for Darcy to have gone looking for her again, and to extend his civilities to the Gardiners. Also, her behaviour might have alleviated him a little. If Lizzy was still set against him, she would have coldly rebuffed his politeness! Her politeness must have given him the courage to introduce his sister to her.