With sound-stage doors made big enough for performing elephants, the century-old Paramount Pictures lot on Melrose Avenue is a living museum of the film business. Now the studio, one of the world’s first—and the last still based in central Hollywood—is for sale. Paramount’s controlling shareholder, Shari Redstone, is seeking a buyer for the teetering empire she inherited from her father Sumner, who died in 2020. For six months suitors…