The 27-year-old has netted 18 goals in just 33 appearances this season to help fire Saints away from the relegation zone.
Lambert told talkSPORT: “I don't think he'll be thinking any down thoughts.
“His mentality is superb, and he'll just be thinking that he's going to carry on what he was doing.
“It doesn't matter when the Euros is going to come, he is good enough to continue his form
“I know he was a Southampton fan and I knew it would come together for him."