"As if [immortality] were our very birthright, which we could not come to grasp the meaning of until this time of middle life when we looked on only as many years ahead as already lay behind us." (1.169)
Immortality gives Louis a unique perspective on mortality. Many people believe themselves to be immortal until a certain age, when that all changes. For Louis, he not only gets to preserve his youthful appearance, he also gets to preserve the reckless abandon that comes with youthful ignorance.
"This was slow decay, the body refusing to surrender to the vampire of time which had sucked upon it for years on end." (1.223)
Louis has a dislike for mortal life. Not that he dislikes mortals, but he seems to dislike the unfair nature of the life cycle, especially now that he has some control over it.
"It was only when I became a vampire that I respected for the first time all of life." (1.351)
You've seen the cheesy movies where the rich person switches places with the poor person from the other side of the tracks. This is like that. Louis only appreciates what he had—real life—once he becomes immortal.
"What does it mean to die when you can live until the end of the world? And what is 'the end of the world' except a phrase, because who knows even what is the world itself?" (1.630)
Immortals quickly lose appreciation for mortal life—and respect for death—because it isn't something they experience often, if ever. Louis sees this attitude as monstrous in Lestat, so he tries his hardest to remind himself of the fragility of mortal life.
"I am not mortal, father, but immortal and damned, like angels put in hell by God. I am a vampire." (1.645)
Here we see Louis confess his immortality to a priest in a confessional. He equates just being immortal with being in sin. Is mortality—or consciousness of mortality—a prerequisite to living a good life?
"How had he come back, how had he triumphed over death?" (2.4)
There are many times throughout the book when Louis wonders if vampires are truly immortal. Lestat is able to survive being burned, buried alive, and eventually burned again. What can kill them?
"'Perhaps [Lestat] was incapable of dying... perhaps he is, and we are... truly immortal?'" (2.22)
One of the reasons there are so many questions about immortality is that Lestat never gives any answers. The rub is that he doesn't know, either. There is no vampire manual.
"'We all die,' he answered her. 'The one thing you share with every mortal is death.'" (3.81)
Why are we talking about immortality when it's clear that even vampires die? Maybe the politically correct term would be "differently mortal"? Even so, if no one actually kills a vampire, then what happens? What makes immortality impossible in that case?
"'Monsters! To give me immortality in this hopeless guise, this helpless form!'" (3.309)
Immortality is definitely a curse for Claudia, because she is forced to spend all her years inside a child's body. Would you want to live forever if it meant that you had to be dependent on an adult for eternity?
"'It's a mortal death, only mortal death.'" (3.362)
Oh, mortals, they die all the time. Vampires only seem to care when another vampire is killed—maybe because it's such a rare occurrence.