The 29-year-old scored twice in Monday's 3-1 win over Plymouth to all but guarantee the Saints an automatic-promotion place after moving three points clear of Huddersfield with a vastly superior goal difference.
And Lambert, who has notched 21 goals this season, believes promotion is a reward for the effort his side have put in over the last 12 months.
"A club like this meant we were disappointed not to get close last season, but I was confident that we could go up this year and we've done it, so I just can't wait now," he told Saints Player.
"I think it's too much for Huddersfield to turn around really. It's something like 17 goals difference so I don't think we're being too premature by celebrating us going up.
"It's been hard for a few weeks and we kept trying as much as we could because Huddersfield kept on winning, but finally we've managed to break free and pass the barrier and we've been absolutely superb."
Source: PA
Source: PA