The Last man is Nietzsche's antithesis of the Übermensch in Thus Spoke Zarathustra. The Last Man sought eternal life at all costs, including costs Nietzsche despised, such as sacrificing love and happiness.
Excerpts from Zarathustra's Prologue suggest that Deleuze's quote may be in reference to the Preachers of Death in I 9. They appear to have the attitude that life is meaningless, and meaning only occurs through death. These preacher's stances reflect Nietzsche's opinion of most religions at the time; Nietzsche had very disparaging things to say about religions such as Christianity.
Interestingly enough, Nietzsche roasted both The Last Man and The Preachers of Death. If I may interpret, the Last Man sought immortality purely under his own power, while the Preachers of Death sought immortality purely under an external power (the power of their deity). Zarathustra preaches against both stances, suggesting Nietzsche viewed the path to the Übermensch as a path somewhere between the two extremes.
I think it would be fair to summarize this towards your question: he suggests one needs both sides of the coin, and it's up to you to self-reflect and observe the world enough to keep them in balance. My favorite wording: "Live every day like it is your last, and look forward to watching the sun rise tomorrow." The joyful challenge is in actually doing it.