Xherdan Shaqiri set the ball rolling with a pin-point free-kick on nine minutes and Takumi Minamino made it two with a similarly spectacular finish into the top corner.
Curtis Jones' quick-fire double put a youthful Liverpool into a four-goal half-time lead, and there was no respite for League One high-flyers Lincoln as Minamino doubled his tally with Liverpool's fifth 18 seconds after the restart.
Tayo Edun and Lewis Montsma scored either side of Marko Grujic's strike as the goals rained down in a frantic seven-minute spell at Sincil Bank, before Divock Origi added Liverpool's seventh in the final minute to send Jurgen Klopp's team into a fourth-round tie with Arsenal in style.