The striker has given his new manager his full backing, saying St Mary's is an "exciting place to be" and is confident the Saints will avoid relegation this season
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However, Lambert is confident the new manager can improve the club's fortunes and says a top-four challenge is not "unrealistic".
"The new manager has been great and you can see since he has come to the club he wants to make things happen," he told The Sun.
"The chairman is very ambitious and Southampton is going to be a very exciting place to be over the next few years.
"It is not unrealistic to try and challenge for the top four over the next three years. That is what we have to aim for.
"Three years ago a lot of people would have laughed in our faces if we had said we'd be in the Premier League.
"We have got to keep that momentum going and keep moving forward. I am very confident we will stay up."