The England international scored the hosts' second goal in a routine 2-0 win over Crystal Palace at St Mary's yesterday, just two minutes after strike partner Dani Osvaldo grabbed his first Southampton goal.
But 31-year-old Lambert knows Saints need to maintain their form if they are to mix it with the big boys at the business end of the campaign.
"A good start is important to any team in any season, but just because we've done well doesn't necessarily mean we can lay off a little bit," he said.
"We'll be trying to improve because we know the teams around us in the league are going to pick up points so it's going to get harder to stay where we are, but we're confident we can do it.
"It's very nice [to be fourth], so let's try to stay there now. It's early doors, so we've got to take our start into the rest of the season and push on so we can stay there."