The 31-year-old Lambert scored the winner on his international bow against Scotland earlier this month and also struck the only goal of the game in Saints' Barclays Premier League opener at West Brom.
Despite Lambert's fine start to the campaign and his 15 goals in all competitions for Southampton last season, Pochettino decided to invest a reported £12.8million fee to bring Osvaldo to the south coast from Roma.
In his current system the Argentinian has room for only one out-and-out striker but he has backed the pair to work together well and believes the signing of Osvaldo could spur Lambert in to getting even better.
"I don't think they are that similar," Pochettino said of the style of his two frontmen.
"I think they could find it very easy to play together. But we will be gauging that as the season unfolds, the Premier League is a tough competition and there are also two cup competitions.
"You also have to think that all great players know how to get along on the pitch and know how to play well together, regardless of the characteristics that they have.
"Rickie has shown time and time again that he is a very intellectual footballer and that he welcomes the competition. He welcomes the fact that Osvaldo is here because it will make him raise his game."
Pochettino, who managed Italy international Osvaldo when the two were at Espanyol, reckons the 27-year-old has developed in recent years, both on and off the pitch.
He was suspended and fined by Roma in 2011 for punching team-mate Erik Lamela during a defeat in Serie A but Pochettino feels he has now moved on from such incidents.
"I worked with him at Espanyol more than three years ago and I think he is a player who has matured in that time," Pochettino said.
"He has grown and progressed as well so overall I think he is a much more rounded player and not just in the football side but also in his personal way of being. It is true that in other countries many times incidents are exaggerated.
"It is clear that players who have character, such as Osvaldo, have a certain character that they need to keep in check. But we have no doubt that he is going to be surrounded by a good group of people and that will enable him to play his best football for us."
Osvaldo became the third summer signing at St Mary's following deals for defender Dejan Lovren and midfielder Victor Wanyama and, although Pochettino said he will be keeping a close eye on the market, he does not expect to make any further additions.
"We are pretty pleased with the players we have brought in and we are not looking that much into other signings," he added.
"But we are also keeping an eye on the market to see if anything arises because different things could actually happen and we need to be able to react fast.
"We are an ambitious club and we have an important project behind us. I think the project is very clear and it is very structured We are also adding into the mix three signings, three important signings that we felt we needed to improve the squad."