It's very much possible that given enough time, lack of sleep can kill you. But, you would be more likely to die from the effects of lack of sleep than from sleep deprivation itself. Research conducted in the 1980s indicated that it is possible to die from sleep deprivation; a group of rats died after 32 days of complete sleep deprivation.
There's a story about a King who caught his wife in bed with another man. Instead of killing him on the spot, this King decided to torture the man by never letting him sleep. He lasted exactly one year. Cruel.