The Justice Department has closed its criminal investigation into whether a disparaging memoir by President Donald J. Trump’s national security adviser John R. Bolton illegally disclosed classified information and dropped its lawsuit aimed at recouping profits from the book, according to two people briefed on the matter and a court filing. The agreement ends an effort that began under the Trump administration to silence Mr. Bolton and sue him over the book’s profits. Ending both the inquiry and the lawsuit is a clear rebuke by Attorney General Merrick B. Garland of the Trump Justice Department’s tactics in the matter. A settlement by the Justice Department is likely to shield Trump administration officials from being forced to answer questions under oath about their time in office. A federal judge had given Mr. Bolton’s lawyer, Charles J. Cooper, approval to begin deposing those officials, but a settlement would end that litigation.