The Argentina winger endured a miserable campaign last season after becoming the club's record signing following his £30 million switch from Roma.
Lamela was bought as a replacement for Gareth Bale, but the 22-year-old has so far failed to justify his huge price-tag.
However, Redknapp, who played for Spurs from 2002-2005, thinks that Pochettino could prove to be the making of Lamela.
Speaking to Sky Sports News, Redknapp said: "I think he can bring the best out of Lamela. Obviously being from Argentina will help. I think we'll see whether [Lamela] has the credentials or not.
"They spent £30 million on him and it's an awful lot of money. It hasn't worked out so far, but [the Spurs hierarchy] may think that [Pochettino] may be able to get the best out of him."
Lamela's disappointing Spurs stay has seen him repeatedly linked with a return to Italy with Inter Milan said to be keen, and a report by ESPN on Monday claimed that the Nerazzurri were preparing to bring him to back to the country where he earned his reputation.
Pochettino signed a five-year on Tuesday evening after leaving Southampton, and the former Espanyol coach arrives at White Hart Lane after guiding an expansive Saints side to an eighth-place finish last season.
However, the former Liverpool captain thinks that while Pochettino arrives in London with a burgeoning reputation, the lengthy deal will ultimately be meaningless if success isn't immediately obtained.
"[The contract] doesn't mean anything at Spurs," Redknapp added. "If Spurs don't finish in the top four this year then he will be under an awful lot of pressure.
"I wouldn't be surprised at all [if Pochettino was under pressure]. It's not the right way to go about it."