By Luc Cohen NEW YORK (Reuters) – Donald Trump on Wednesday lost a bid to delay a defamation lawsuit brought by the writer E. Jean Carroll after he denied having raped her, ahead of a deposition of the former U.S. president scheduled for Oct. 19. Carroll sued Trump in November 2019, five months after he denied raping her in the mid-1990s in a Manhattan department store dressing room. Trump said “she’s not my type.” More recently, Trump also claimed that he was shielded from Carroll’s lawsuit by a federal law immunizing government employees from defamation claims. Trump in September sought to p…