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[Harry Potter] Can someone explain to me the “always” scene?

I must be really dense but I didn’t get the scene. Did Snape mean it as in he always loved Lily, or was it for Harry?

Because Dumbledore already knew Snape loved Lily, I remember in the book that it was something he already figured out. So it didn’t make sense that when Dumbledore asked “after all this time...” since Snape would always love her, but the scene fit Harry more...since Snape was a dick to him all his life.

But then Snape’s response didn’t make sense if it was directed at Harry since Snape didn’t ALWAYS like him. Was that scene meant to show he DID like Harry but never revealed it and just acted his part? 

I’m just confused if it was directed at Harry or his mom.
gpt
If memory serves, it was a response to Snape's patronus; a doe, the same as Lily. Even after all the things that had happened, he could still call on his memories of her as the source of the sort of pure feelings and emotion needed to perform the charm. After she left him for his childhood bully, after he lashed out against her for being muggle born, after falling in with Voldemort himself, after all that time...

Dumbledore knew that Snape loved Lily, but on some level assumed that Snape's continued aid against the Death Eaters was chiefly revenge for hurting him. The patronus was proof positive that his assumptions weren't full-on accurate.