Nine months to the day he was appointed, the German committed his future until 2022 on Merseyside after owners Fenway Sports Group declared their desire to reward him for the improvements the club showed in his first season.
Klopp took the Reds to two cup finals last term and brought performances and results out of a squad previously believed to be substandard.
Midfielder backs Klopp to enjoy successful Anfield stay
Lucas, who earlier last week suggested that the eight-month period the squad had under Klopp last season will be "a big advantage" in 2016-17 in that they're already adjusted to his style, explained why he's delighted to see the Reds boss commit to the club for an extended period.
"It's great news for the club and for the fans as well," the Brazilian insisted, citing "the relationship" Klopp has with the club's supporters after they "started really well" together back in October.
Lucas explained that the players hope that Klopp "will have a lot of success at the club", speaking to Liverpoolfc.com and acknowledged that they "got to two finals last year" just "eight, nine months" after he was appointed.
"And of course, this is the first full season we will have under him," he continued, looking towards the coming campaign. He insisted that the new contract is "always good" because it demonstrates the club's belief "in what he is doing and the decisions he is making."
The long-serving defensive midfielder, who at times filled in at centre-back last term, insisted that Klopp is "trying to change things step-by-step without affecting the team so much" as he lauded his managerial abilities.
Lucas on the verge of leaving Liverpool this summer?
Lucas, whose place in the squad once again appears under threat, will become the club's longest-serving player by some distance when Martin Skrtel expectedly seals his £5.5 million transfer to Fenerbahce.
But his experience, which has seen him survive four managers since signing for the club in July 2007, will not guarantee his safety from the cull as Klopp looks to minimise his squad.
The 29-year-old was earlier linked with a move to Besiktas, whom he was reportedly on the verge of joining last season before an excellent performance away at Arsenal early on in the Premier League season convinced then manager Brendan Rodgers to intervene.
With Klopp looking at midfielders Mahmoud Dahoud and Piotr Zielinski, although moves for both have made no real progress in recent weeks, Lucas' chances of starting a 10th consecutive season with the club look less and less likely.
After starting just eight league games since the turn of the year, he recently admitted that he still does "not know exactly what will be my role within the group."
However, the fact Lucas' captained Liverpool's first-half team in their opening pre-season friendly victory over Tranmere Rovers on Friday suggests he might be given the opportunity to prove his worth to Klopp.