The England veteran believes his international teammate has found the belief he requires at Liverpool after struggling for opportunities at Stamford Bridge.
The England striker left the Blues in January 2013 and has gone on to score 31 Premier League goals in just 37 starts for Brendan Rodgers's side.
That form has seen him called up to England's World Cup squad for the upcoming tournament in Brazil, with the former Manchester City prospect seen as a key figure in Roy Hodgson's side.
And Lampard said he is pleased for his international teammate after seeing him grow frustrated at a lack of first-team opportunities at Chelsea.
"I’m really pleased for Studge [Sturridge] because, at Chelsea, I think he was a bit frustrated. He felt he could have played more," he told the Sunday Mirror. "He felt the position he was playing in was one he wasn’t happy with and he felt it was good for him to move.
"It was maybe not good business for Chelsea. It looks bad when you look back, but, at the time, you never know. Individually, for him, it was a good move. He has gone from strength to strength. I think he does get the credit he deserves now, but with what Luis Suarez does alongside him at Liverpool, maybe that takes the edge off the praise.
"Studge has got that inner-belief and no wonder, because he is one of the sharpest players I have seen off the mark, with his quick feet around the box and he gets his shots away, he is very difficult to defend against. I think he is comfortable at Liverpool."