In "Pride and Prejudice," what is Elizabeth's initial reaction to Darcy's letter about Lydia? How is her opinion of him changing?

This turning point can be found in XIV, Vol II (or Chapter 37).

Elizabeth is initially incensed by Darcy's intrusion, then considers her own family's ill behavior. The realization of how the Bennets must appear to the world at large makes Lizzy feel ashamed and abashed. However, despite this softening, she is still unable to give Darcy her approbation:

"She studied every sentence and her feelings towards its writer were at times widely different. When she remembered the style of his address, she was still full of indignation; but when she considered how unjustly she had condemned and upbraided him, her anger was turned against herself; and his disappointed feelings became the object of compassion. His attachment excited gratitude, his general character respect; but she could not approve him; nor could she for a moment repent her refusal, or feel the slightest inclination ever to see him again. In her own past behaviour, there was a constant source of vexation and regret; and in the unhappy defects of her family a subject of yet heavier chagrin."

Elizabeth has not yet conquered her own pride and prejudice, but she is relenting, and Darcy is doing the same. This scene is a crucial moment in the series of walls that must be felled in order for the happy ending to occur.