Next week's Europa League clash against Chelsea will be the Aguias' ninth major UEFA final in their long and illustrious history.
However, they have lost the previous six in succession and last tasted success on the continental stage back in 1962.
Back then, Eusebio inspired Benfica to a 5-3 European Cup triumph against Real Madrid at the old Olympisch Stadium in Amsterdam.
Now, 51 years on, the Portuguese giants return to the Dutch capital hoping for more success in a European showpiece, this time at Ajax's Amsterdam ArenA.
Having not even reached a European final in 23 years, attacker Lima is well aware of the game's importance to the club.
"Not only is the game important for the fans, who have waited so long for a European competition title, but I also believe it would be very important for the players to leave their names in a European competition," the Brazilian said.
"It's very important for them as well and the fans can expect a group and a team who are very much focused on making that possible, but they know that it won't be easy for us."
Portuguese sides have enjoyed a fair amount of success in the Europa League in recent years.
Sporting Lisbon exited the competition at the semi-final stage last season, while in 2011 Porto won an all-Portuguese final with Braga in Dublin.
Lima, like Benfica goalkeeper Artur, was part of the defeated Braga side that night and is looking forward to representing his adopted homeland again.
"I feel very happy to be able to play in Portuguese football and at good clubs in Portugal," he told www.uefa.com.
"That is certainly also the case in European matches and it is very satisfying for me to represent Portugal in those competitions as well."
Overcoming the Blues, though, will be no mean feat.
Last season, Chelsea overcame Porto over the two legs of their quarter-final clash in the Champions League - a competition the west Londoners went onto win.
Lima, one of a number of South Americans in the Benfica squad, is well aware of the threat they pose but hopes Amsterdam will play host to another of the club's finest hours.
"I think the level of confidence increases with every match, with every knockout match Benfica compete in," he added.
"The team is already aware of Chelsea's football and the way we have to face our opponents.
"I think we are prepared to continue that path and continue on with that same strong rhythm to try to bring happiness to our fans."