Re: No, no, Lily. You misunderstand me, I believe

It might not be a determination to propose again, but Darcy does say this about Elizabeth's visit to Pemberley, in the same chapter you quote: "...I hoped to obtain your forgiveness, to lessen your ill opinion, by letting you see that your reproofs had been attended to. How soon any other wishes introduced themselves I can hardly tell, but I believe in about half an hour after I had seen you."

Lady Catherine's visit may have give him determination, but the desire was certainly there at Pemberley, even if he thought it was hopeless.

For the record, I don't actually think he was intending to propose that morning when he came upon her with Jane's letters, but he did have a habit of seeking her out, often alone, at Rosings. At Rosings, he thought she enjoyed his company and wanted it. Cal makes a good point about him not knowing for sure how she feels about him, because it's possible she's just being polite to him in front of his guests. But that trip to Lambton says to me that he wanted to see her on more neutral ground, to see if this time she would welcome his company. He couldn't do that at Pemberley any more than he could court her in front of Lady Catherine, so once more he had to seek her out elsewhere, and alone.