In The Sandman Presents: Lucifer - The Morningstar Option #3 (written by Mike Carey and drawn by Scott Hampton), Lucifer explains he needed Rachel Begai to channel her desire to destroy the Velleity, as he himself is short on desire:
At that point Lucifer has his hidden agenda, namely getting the Letter of Passage from Yahweh - he wouldn't go to all the trouble of fighting the Velleity otherwise.
Getting the Letter serves other means - breaking free of Yahweh's Creation, and of his omniscience and omnipresence. This is what Lucifer wants, or desires (as explained later, from the start of creation) - he doesn't show interest in anything else, and everything he does in the Lucifer comics series is for that one goal.
This was also acknowledged in the last issue of the series:
So why is Lucifer short on desire? How does that fit in the rest of the series? Is my understanding of his character wrong?