Joined by his fellow Brazilian in Klopp’s forward line, Coutinho showcased a strong relationship with Firmino.
The 24-year-old returned to Melwood on Monday morning for pre-season training, and Klopp will be looking for more of the same from his key duo.
Speaking this week, Lucas hailed his countrymen, and backed them for a “big season” under the German on Merseyside.
“He had a very good season last year, but normally in your second season you get better, you play better,” Lucas said of Firmino.
“He knows the team now, he knows the players—he’s got a good connection with some players already, so we hope he can maintain the level of performance he had last year and hopefully even improve.
“I think he showed in many games that he can be a very important player for us and hopefully that will be the case this year.”
Coutinho has been linked with moves to Barcelona and Paris Saint-Germain this summer, but looks poised to remain with Liverpool.
The No. 10 impressed for Brazil at this summer’s Copa America Centenario, despite Dunga’s side crashing out in the group stages following defeat to Peru.
Scoring an excellent hat-trick in Brazil’s 7-1 win over Haiti, Coutinho announced himself on the international stage, and Lucas said the former Inter Milan playmaker would “come back with a lot of energy” as a result.
“Brazil had a very bad tournament, it didn’t go well for them, but Philippe—I would say he had a very good tournament, he was probably the best player for Brazil,” he continued.
“He scored a hat-trick, and I think he left of course disappointed, but happy with the way he played.
“It’s another big season for him. He showed in the last two or three years that he can be the difference in our team.
“I’m sure he will come back with a lot of energy and looking forward to starting again.”
Coutinho could return to action for Liverpool against Fleetwood Town on Wednesday night (7pm kickoff BST), and is likely to be joined by Firmino and £30 million summer signing Sadio Mane.
Mane impressed on Friday night against Tranmere Rovers, and will hope to continue to build chemistry alongside his attacking colleagues ahead of 2016/17.