Standard Sport understands that Kepa faces an uncertain future at Stamford Bridge, while Burnley and England keeper Nick Pope has reportedly been flagged as a possible replacement in the summer transfer window.
Kepa should have saved Isaac Hayden's header that stole Newcastle a 1-0 victory in injury time on January 18, while he could not even lay a glove on Hector Bellerin's late equaliser in Tuesday's 2-2 draw with Arsenal.
The former Athletic Bilboa star currently boasts the unwanted tag of the lowest save percentage in the Premier League, and Lampard has told him to go back to basics to return to top form.
"Well he will have to deal with outside criticism; that is what football is," said Lampard.
"Every player, no matter great you are in your career, the best, the absolute best of all time will get criticised and you have to deal with it.
"I think with Kepa he knows, he'll be honest that there have been some mistakes that have cost us goals.
"It is the nature of it, so that needs to improve. Goalkeepers may have slightly more spotlight on them, but it is a similar thing, really. I think the important thing for that is not to get too embroiled in what is said on the outside and look at your own game.
"It is always the basics, how hard can I work. That's not just for Kepa, but for any player.
"If you feel in a lack of form, fight to get it back. Go back to basics."
Regarding Chelsea's reported interest in Burnley keeper Pope, Lampard says he is not seeking to add another body between the sticks this month.
Asked if he wanted to recruit another goalkeeper, Lampard added: "I am not looking at it now.
"I am not affected by criticism from the outside as much. I am aware of it, not affected by it."
Lampard also said he is not interested in a move for Lille's France Under-21 midfielder Boubakary Soumare.
"I'm aware of him as a player, but he is not on our radar for this window," said Lampard.
"We played against him, but he is not one on the immediate radar.
"He is a good player, but he is another club's player."
Additional reporting by PA.