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.
After minor league sides LincolnCity and Sutton United produced upsets to enthuse romantics on Tuesday, the mantle was passed to Plymouth to make another stand for the smaller clubs.
Despite their dogged resistance, however, there was to be no shock at Plymouth's HomePark or at St Mary's where Premier League Southampton edged past second tier NorwichCity 1-0 after Shane Long scored in the second minute of stoppage time.
Newcastle United's 3-1 victory over BirminghamCity in an all second-tier clash completed the third-round fixtures.
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.
The visitors had an early penalty appeal waved away when Daniel Sturridge had his legs swept away from beneath him by Oscar Threlkeld, but they did make a breakthrough after 18 minutes and it came from an unlikely source.
Lucas had not found the net since a Europa League clash against Steaua Bucharest in 2010, but he was allowed to rise unchallenged to head in Philippe Coutinho's whipped corner at the near post.
Plymouth then 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 Juergen Klopp's side who will face Wolverhampton Wanderers in the fourth round.
"Maybe it was not the most exciting game, but for us it was very important," Klopp told BT Sport.
"I love this in football, everybody can cause everybody problems."
Southampton's clash with Norwich was a dour game that had looked destined to go to extra time until Long scuffed the ball home deep in stoppage time from a metre out.
Newcastle United beat Birmingham thanks to an early penalty from Matt Ritchie and a superb finish from Yoan Gouffran to give them a two-goal lead at the break.
David Cotterill pulled a goal back for Birmingham, but Ritchie's late second from close range wrapped up the win for Newcastle.