The novelist William Styron has a string of best-sellers to his name — Lie Down in Darkness, published when he was only 26, The Confessions of Nat Turner (which won the Pulitzer), and Sophie's Choice. But Styron's later years were a struggle.   He fell into a severe depression, was an alcoholic, and did not publish another novel in the 25 years before he died, in 2006.   A new memoir by his daughter Alexandra gives us the fullest, and certainly the most intimate, picture yet of his life before and after.   It's called Reading My Father. She found several manuscripts that her father wasn't able to finish.   "I didn't realize how hard he had tried to pull out of his soul another great novel," she tells Kurt Andersen.   "All of a sudden, I thought: 'This is horrible, and this is the key to the story of what happened to Bill Styron.'"    Cover art from Reading My Father, by Alexandra Styron

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