The Manchester United forward has struggled to impose himself at international tournaments since exploding onto the world stage at Euro 2004.
His performance in England's opening Group D defeat to Italy, in which he produced a patchy display in an unfamiliar left-sided role, last Saturday has come under the microscope in recent days.
Rooney on Tuesday hit out at media speculation over the reasons for him undertaking extra sessions at England's training base, and Lampard proceeded to add his name to the raft of players from Roy Hodgson's camp to back the 28-year-old.
"Unfortunately we do have a fixation with one player during every World Cup, pretty much - the ones that I've been involved in," said Lampard.
"It's a bit frustrating when you're in a team group and that happens because we're there trying to play together.
"People are not selfish in this squad. We're trying to get results and then a fixation with one player can become, rather than a debate, a bit of an agenda.
"So I think we do need to drop the agenda and look at the team, whoever plays.
"The manager will pick the best team that he sees fit and, whoever plays, we want to win the game."
The form of Liverpool youngster Raheem Sterling, who excelled in the "number 10" role against Italy, complicates the equation for Hodgson amid calls for Rooney to be utilised centrally when England face Uruguay in Sao Paulo on Thursday.
But the 19-year-old told a Tuesday press conference that he would be happy to revert to the flanks in a bid to spark a winning combination with Rooney.
"It’s up to the manager to decide, at the end of the day, but that’s my normal position out on the wing," Sterling said. "So his vision and his passing ability and my running abilities (together) could be a really good thing."
Sterling also paid warm tribute to Rooney’s influence on his fledgling career over recent weeks.
He added: "Some of the stuff he does with the ball, you try to take little clips out of his play and really learn from that.
"He's a world-class player. I've watched him growing up and it's someone I look up to, so to train with him now in this training camp over the last couple of weeks has been a real honour.
"He works really hard and he's always improving as well. Someone like that, for me to look up to, I'm really glad to have him in the team."
