You can’t die from lack of sleep. Except when a genetic mutation prevents you from sleeping at all.
Fatal insomnia is a horrible disease, one of the more brutal maladies that we know about. Essentially, a mutation of a specific gene causes a protein to mis-fold (remember protein folding?). And that protein messes up the function of the thalamus part of the brain, in such a way that it becomes increasingly difficult to sleep.
What ensues is a slow slide downwards as the symptoms get worse and worse. For the first four months you can still sleep intermittently, but as the insomnia grows you develop general paranoia and start having panic attacks. Hallucinations increase, weight decreases, and eventually you go into permanent hypnagogia.
Hypnagogia is that weird liminal time right before you fall asleep. You’re not actually asleep, but you’re not exactly awake. Auditory and visual hallucinations are common, like flashes of light or noise. If you’ve ever felt like you’re falling and then jerk yourself awake, you were probably in a hypnagogic state. Now imagine feeling that way without end. Twitchy hallucinatory half-sleep forever.
There’s no cure for fatal insomnia. It’s extremely rare, fortunately, but on average people die within 18 months.