It's certainly possible to die when you don't get enough or any sleep.
But to die from lack of sleep itself you'd have to stay up for at least 2 weeks straight without any sleep at all and during that time your body starts to shut itself down if you don't get any sleep during that time.
And when your body shuts down from lack of sleep you're likely to sleep for good when you do go to sleep finally.
It's never a good idea to stay up all night just for the fun of it or because you want too or need to get something done.
When you don't have enough sleep your body cannot function properly and repair and recharge itself.
Our brains are recharging while we're sleeping and when we don't get the required amount of sleep our brains cannot recharge and we lose memory and concentration.