The midfielder has started well under the German and his former teammate has backed him to be a great player.
Lallana has started both of Klopp’s first two games in charge and has been more than impressive, with him leading the pack as he tirelessly closed down everything against Spurs.
He then turned into creator general in the 1-1 draw with Rubin Kazan as most of their chances came through the attacking midfielder in a disappointing evening for the side.
Lallana has had a difficult time at Anfield since joining from Southampton, but Lambert believes he will come good under Klopp’s leadership.
"I think Adam will do really well under him," he told LFCTV.
"Obviously it's hard to become a regular in the Liverpool team because there are so many good players, especially in his position. But if he gets a good run of games I truly believe he could be a great, great player. “
At this moment in time, there is the opportunity for Lallana to stake a claim to a first team place under Klopp.
He has struggled with injuries since joining last summer, meaning he has not been able to get a consistent run of games in the side, while Philippe Coutinho is the first choice player in the number ten position.
However the Brazilian is struggling for form this season, and Klopp is well known for picking players on their suitability to the system he wants rather than previous form or ability.
And Lallana has certainly shown his desire to impress in those first two games, with his running in the game against Tottenham a clear indication he has bought into the German’s philosophy early on.
If he can get in the side and find a run of form, there is every chance he can be a top player for Liverpool under their new boss.