In DH, when Harry reviews Snape's memories after Snape is killed in "The Prince's Tale" chapter, he sees Snape telling Dumbledore (
There was a long pause, and slowly Snape regained control of himself, mastered his own breathing. At last he said, “Very well. Very well. But never—never tell, Dumbledore! This must be between us! Swear it! I cannot bear . . . especially Potter’s son . . . I want your word!”
“My word, Severus, that I shall never reveal the best of you?” Dumbledore sighed, looking down into Snape’s ferocious, anguished face. “If you insist . . . ”
Yet... when he's about to die, he - the master of Occlumency and of his own brain - dumps to Harry all his memories, instead of just the critical one Dumbledore needed of him (the information about Harry having the last piece of Voldemort's soul in him), including:
All the information and emotions about how his feelings for Lily grew
Even the very conversation with Dumbledore after Lily's death that results in the bolded quote above.
Is there any indication in canon (books/interviews/Pottermore) as to whether this was a deliberate action on Snape's part, to include the full information to Harry in his memory dump; or was it not by Snape's design?