Carragher seems positive over Lambert's signing.
The 32-year-old signed for Liverpool from Southampton in a deal that is said to be worth around £4.5 million, becoming the Reds first signing of the summer, and it meant they were bringing back a player who left Liverpool at the age of 15, and had to climb the Football League ladder.
During his two seasons in the Premier League on the South coast, Lambert has managed to tally double figures in each of those two campaigns.
Carragher is quoted by the Liverpool website, saying: “I think it’s a very good signing. He’s a local boy, a Liverpool fan, and it’s probably been a dream for him.
“There’ll be lots of games with Liverpool being involved in the Champions League, so he’ll play his part and I’m sure he’ll get some goals.”
Lambert scored his first goal since he made the switch to Liverpool for England last night in their 2-2 draw with Ecuador as part of their preparations for the World Cup in Brazil.
The Kirkby-born striker is likely to provide cover for Luis Suarez and Daniel Sturridge in most games next season, with Italian striker Fabio Borini - who spent the past season on loan at Sunderland - likely to be competing with Lambert.