The Wales international, who became the most expensive player in football history in 2013, has struggled in recent weeks after being jeered by sections of the Bernabeu crowd.
Bale has struggled to make an impact in the Champions League last-16 first leg against Schalke on Wednesday night, leading Lampard - who was working for Sky Sports as a pundit - to encourage the former Tottenham star to lose some of his niceness.
Lampard: Bale must become more selfish
“I get the feeling he is a nice boy,” Lampard told Sky Sports. “There is a bit of ego and he should have some because of what he has achieved in the game, but maybe there is a moment when he thinks ‘should I go for goal and take it on or should I look for the other option in case I get criticised?’
“I hope that goes out of his game very quickly because if that is there it is going to affect him.”
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Lampard urges Ronaldo to set record straight
Lampard has also called on Cristiano Ronaldo to publicly confirm that there are no underlying issues between himself and Bale, believing this could help the latter to rediscover his best form.
"If he hasn’t passed to Cristiano (Ronaldo) once and it’s not come off and there are a few boos then it’s only going to be detrimental to the team and to those two as individuals," Lampard added.
"I would like to see Cristiano come out and say there is no issue because he is the boss really and he maybe needs to say that.
“He (Bale) might come through this phase even stronger. He might beat three players next week and put it in the top corner."
Bale struggling to win over Real Madrid fans
Bale has struggled to produce consistently outstanding performances so far this season, but has still managed to score 14 goals in 33 appearances.
He was even more effective in his debut campaign at the Bernabeu, netting 22 goals in 44 matches, while helping Los Blancos win their tenth Champions League title in the process.
Bale also scored the winning goal in the Copa del Rey final - against Barcelona - courtesy of a magnificent solo effort.
But despite last season's heroics, the Real Madrid faithful are a notoriously demanding bunch and haven't entirely taken Bale to their hearts - as the whistles this season have proved.
Manchester United speculation
Subsequently there has been much speculation in recent weeks and months that Bale could return to the Premier League in the not-too-distant future.
Manchester United have been strongly linked with the 25-year-old, who won the PFA Players' Player of the Year award in 2011 and 2013, but Real Madrid are understood to have no plans to offload the Welshman this summer.
Bale was at his brilliant best during his final season at White Hart Lane, when he scored a magnificent 26 goals in 44 matches as Tottenham's main man.
Bale can become Real Madrid's main man
Lampard is on the right lines when he says Bale must become more selfish. It's important he plays his natural game and doesn't concern himself too much with Ronaldo's individual objectives.
Ronaldo is still very much top dog at the Bernabeu - but the Portuguese star is now on the wrong side of 30, and Bale has the quality to overtake his teammate as the best player at Real Madrid.
He just needs to believe in himself a little bit more.
Is Lampard right: does Gareth Bale need to become a little bit more selfish? Should he leave Real Madrid? Have your say in the comments below!