The 26-year-old Uruguay international returned to Premier League action at Sunderland on Sunday and helped himself to a trademark double in a 3-1 victory at the Stadium of Light.
It was his first league appearance since he was banned for 10 games for biting Chelsea defender Branislav Ivanovic last season, and provided him with the opportunity to celebrate the arrival of his baby son Benjamin.
But more importantly, his contribution on Wearside confirmed that he had lost little of his potency during his enforced lay-off, during which he stunned the club by asking to leave Anfield.
Lucas told the club's official website www.liverpoolfc.com: "Luis has just become a father again and for him to celebrate with two goals, I am very happy for him.
"He is showing again just how good he is. He is a world-class player and it is so important to have players like that if you want to fight for good things this season.
"Hopefully he will have another fantastic season for us like he did last year.
"Luis showed with his performance that he is really committed to the team and to the club. He just wants to help us, and we will try to help him too."
Suarez, who had played in the Reds' 1-0 League Cup defeat to Manchester United in midweek, needed just 37 minutes to make his mark at Sunderland, turning up in the right place at the right time to stab home Daniel Sturridge's cross.
Sturridge had earlier given the visitors the lead when he bundled Steven Gerrard's corner over the line with his arm and after Emanuele Giaccherini had pulled a goal back for the Black Cats, the pair combined once again at the death for Suarez to complete his double.
Manager Brendan Rodgers later praised his front two and suggested there is not a better pair in the Premier League, even though their partnership remains in its infancy.
Lucas said: "When Dan arrived here, within a few months Luis got the ban, so they didn't have much chance to play many games together.
"But you could see how well they linked up. The understanding between them is really good and it will only get better.
"It will improve over the course of the season and hopefully they will keep helping us with goals and assists.
"It was really important for us as a team that we got back on track with a win.
"To lose at home to Southampton was really disappointing and we didn't perform the way we should have done. At Old Trafford, we played well but didn't get the result.
"This was a great game for us to respond. After going 2-0 up, we knew they would come back at us at the start of the second half.
"They got back into it, but after they scored we controlled the game quite well.
"We were solid defensively and then we got a brilliant goal on the counter-attack to kill the game off. Overall we deserved the victory and the three points have moved us back up the table."
If Suarez inevitably snatched the headlines, Sturridge's performance was equally impressive and Rodgers could not hide his delight at the 24-year-old's efforts.
He said: "All Daniel needed was an opportunity to play. He needed confidence, like any player.
"When he played at Chelsea, he was coming in and he had to really make an impact and probably the only way he felt he could maybe make an impact was to get goals.
"We have done a lot of work on his game. He is not an out-and-out number nine, he is a player who can play and move and he can drop in short and go behind.
"But what is important he understands is that I will allow his talent to flourish, but he has to also understand that it's for the team.
"You only need to look and see how hard he is working, how hard he presses the game. He is an outstanding footballer who when he is not on his game, he's good, but when he's on his game, he's phenomenal.
"He is an outstanding talent and England are very fortunate to have someone of that quality."
Rafarazi - thats how F365 saw it, objectivity has no place on this site- sanity1892