Lemuel Cook, 1759-1866, could very well have known a Civil War veteran, who could very well have known a WWII veteran, who could very well survive today.
My grandfather's grandfather was born in 1780--he was three years old when the Revolutionary War ended. I knew my grandfather but he didn't know his grandfather, who died before he was born.
The last Civil War veteran died in the 1950s so undoubtedly many World War II veterans knew a Civil War veteran. When I was a child I knew an old woman who was born in February 1869--if Lincoln had not been assassinated he would still have been President when she was born.