With Steven Gerrard set to miss matches against Fulham and Queens Park Rangers following shoulder surgery, Carragher is likely to captain the Reds in his final two outings for the club ahead of his retirement this summer.
Lucas believes the 35-year-old skippering the side will be an apt tribute.
He told Liverpoolfc.com: "He deserves it, really. He has had an awesome career and for I don't know how many years he has been playing for the first team.
"He is an example. If you want to succeed as a Liverpool player, you need to really watch him and follow what he does - not just on the weekend, but on a daily basis.
"He is a great professional and the next two games, the armband will be a reward for him for what he has done and he'll retire on a high."
Though overhauling Everton into sixth place is the best Liverpool can hope for in the remaining two matches, Lucas insists Carragher will play the games in trademark style.
"He has been so successful so two wins would be perfect for him and perfect for the team," he added.
"Maybe our league position won't change if we win the next two games, but when we play for Liverpool, we have to approach every game the same way."
Meanwhile, Lucas has paid tribute to the form of Gerrard, who has been one of Liverpool's outstanding performers in 2012-13.
Prior to the news he requires an operation this week, the 32-year-old had started every Barclays Premier League game this season.
"I have been watching Steven in probably his best years for the club, so I am not surprised by what he has done," said Lucas.
"It was important to keep him really fit and playing every game. That shows how much he looks after himself.
"He'll probably be fit next season and we hope he can produce the same performance because it will be a big help for the team."
He continued: "He's been involved in every game this season, but in the next two games we won't have him. He is the captain and a leader, so the team will miss him for sure.
"But we have the experience of playing without him from previous seasons when unfortunately he picked up injuries. We were able to get some good results, so we just hope we can end the season with two wins and look forward to next season with everyone fit. I hope he can recover very quickly."
The absence of Gerrard could present an opportunity for one of the younger members of the squad to step into the first team - and Lucas is urging the Reds' starlets to take any chances that may come their way.
He said: "We don't know yet what Brendan will do in terms of the team for the next two games, but there is an open space for some young players to come in and have the chance to play.
"A lot of young players have had the opportunity to play this season and a few of them did very well, so it's another chance for someone to come in and do right and keep getting experience for next season."