The England striker left the Blues in January 2013 and has gone onto score 31 Premier League goals in just 37 starts for Brendan Rodgers's side.
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And Lampard admitted he is pleased for his international team-mate 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."
Lampard, who has announced that he will be leaving Chelsea after 13 years with the club, feels that the belief that Sturridge has found since he moved to Merseyside has played a major part in his improved record.
"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.
"At Chelsea and struggling a bit to get in the team and then he goes and he has a lot of belief in him there at Liverpool, you can see Brendan Rodgers really trusts in him, he started scoring and he hasn’t stopped.”