The novel in the Elvis Cole series that follows "L.A. Requiem" is "The Last Detective." There was a four-year gap between the publication of the two novels; "L.A. Requiem" appeared in 1999 and "The Last Detective" was first published in 2003.
Robert Crais published two books in between "L.A. Requiem" and "The Last Detective." These were "Demolition Angel" in 2000 and "Hostage" in 2001. Though not directly died to the Elvis Cole series, both novels feature similar themes and character types. When he returned to the Cole series with "The Last Detective," Crais incorporated Carol Starkey, the main character of "Demolition Angel."