If Dennis Lehane’s latest book sounds familiar, that’s because it is. The celebrated author of “Mystic River” and “Shutter Island” is turning a screenplay he wrote for “The Drop” into a paperback novel, due in August. The screenplay itself was inspired by an earlier Lehane short story called “Animal Rescue,” about a killing that results from a lost pit bull. And that, believe it or not, was based on a book Lehane started more than a decade ago but shelved. “Early this year, my publisher asked me to consider writing a novel version, which I normally would have balked at,” Lehane explained in an e-mail. “But there was all this stuff I loved from the original novel and then all this other stuff I loved that got cut from the script and still more scenes I loved that ended up being cut from the film itself, and I thought it might all make a really cool book.” The movie “The Drop,” to be released in September, is notable for being James Gandolfini’s final film. (The “Sopranos” star died of a heart attack last summer.) Directed by Michaël R. Roskam, whose 2011 movie “Bullhead” was nominated for an Oscar, “The Drop” stars Gandolfini as a Brooklyn bar owner involved in organized crime. It costars Tom Hardy and Noomi Rapace. Not one to rest on his laurels, Lehane is also writing episodes of HBO’s “Boardwalk Empire” and working on “Ness,” a prospective TV project about famous fed Eliot Ness.