The Imps beat Premier League outfit Burnley to earn their spot in the draw and have been rewarded with a tie against the Premier League giants, who beat Lincoln's non-league rivals Sutton United on Monday evening.
Elsewhere, Chelsea and Manchester United will battle it out in a titanic all-Premier League tussle at Stamford Bridge, while Tottenham Hotspur will host League One Millwall.
And in the other tie, Middlesbrough will play either Huddersfield Town or Manchester City at the Riverside
FA Cup quarter-finals draw in full:
Chelsea v Manchester United
Tottenham v Millwall