Bale has been made a scapegoat for Madrid fans and press in the Spanish capital in recent weeks, with the Wales international criticised for not passing to star team-mate Cristiano Ronaldo in some matches.
Manchester United have emerged as a possible destination for the 25-year-old, who struggled to make an impact as Real defeated Schalke 2-0 in the first leg of their UEFA Champions League last 16 tie on Wednesday.
Lampard feels that in order to succeed Bale must not second guess himself in the final third.
"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."
Fans booed Bale during Real's 3-0 win over Espanyol last month for shooting instead of passing to Ronaldo, while he was also targeted by supporters in a 4-1 victory against Real Sociedad.
Real boss Carlo Ancelotti has come out in defence of Bale amid rumours of a falling out between the Welshman and Ronaldo.
But Lampard believes the Portugal captain should publicly deny there is an issue.
"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," the City veteran 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."
