Lucas ended a goal drought stretching back to 2010 and Divock Origi missed a late penalty as Liverpool beat fourth tier Plymouth Argyle 1-0 in an FA Cup third-round replay on Wednesday.
Having been held to a goalless draw at Anfield 10 days ago, Liverpool again found Plymouth to be stubborn opponents who made light of the 67 places between the sides in the standings.
Plymouth come close
Having conceded early, when Lucas headed home from a corner, Plymouth frustrated their Premier League visitors for most of the match and almost snatched a leveller when Jake Jervis shaved the post late in the second half.
Origi had a tame penalty saved by Plymouth keeper Luke McCormick in the 86th minute, but there was no late sting in the tail for Jurgen Klopp's side who will face Wolverhampton Wanderers in the fourth round.
Southampton striker Shane Long scored in the second minute of stoppage time to secure a 1-0 win over second tier Norwich City in a dour game that had looked destined to go to extra time.
Newcastle United came through an all second-tier clash against Birmingham City 3-1 thanks to an early penalty from Matt Ritchie and a superb finish from Yoan Gouffran.
David Cotterill pulled a goal back for Birmingham, but Ritchie's late second from close range wrapped up the win for Newcastle.