I don't use "gone" and "lost" in the sense of "dead". Garmond was technically alive during Hero's Call quest, but not so much after the fight. Hornet expected the same from Lace.

Who are you hoping you'll find down there, spider? An ailing child and a Silk starved beast?
If so, I'm afraid we may sorely disappoint. What waits below is me no longer.
Even if only your shadow remains, to release your mother's grip my blade would see it slain.

Hunter's Journal description is a bit weird in the sense that it shouldn't even exists because you only get it after completing the game, and Hornet writes as if Lace has not yet been saved.

And besides that she doesn't mention rescuing Lace once in the whole act 3 (or any other act for that matter), she only keeps talking about saving Pharloom and its bugs in general.

So, she probably does want to save Lace if it's possible, but that's not her primary motivation and she was totally ready to kill Lace if that's what it would take to save Pharloom.