England striker Lambert signed for his hometown club in June after a prolific five-year spell with Southampton.
The Kirkby-born forward was unable to prevent Liverpool from slipping to a 3-1 defeat to Manchester United in the International Champions Cup final in Miami on Monday.
Sterling has found the net twice in the pre-season tournament after a 2013-14 campaign that saw him find the net 10 times and establish himself as a key member of a Liverpool side that narrowly missed out on winning the Premier League title.
The performances of the 19-year-old led him to be selected for the England squad for the World Cup alongside Lambert.
And, after witnessing Sterling's talent first hand as a club-mate, Lambert believes the Jamaican-born star can have an even bigger impact in the coming season.
"I've been really impressed by [Sterling] on this trip and if he keeps on progressing the way he has done over the past year or two he's going to have an unbelievable season," Lambert told Liverpool's official website.
"I don't want to put pressure on him but I think he can handle anything that comes his way. He's a top lad as well.
"Nothing fazes him and that's full credit to the management. The manager has created an environment for the young kids to go and thrive and you can see the benefits of that."
Lambert has been similarly impressed by Daniel Sturridge, who is set to lead Liverpool's line following the departure of Luis Suarez.
"We played and trained a bit together with England so I kind of know Daniel's game," Lambert added.
"I'm learning more and more about him each day. He's a special player and has got so much about his game.
"He's a top player and it makes my job a lot easier playing with someone as good as that."
