A 15-point lead over basement boys Dundee now stands at just eight following the Buddies' 3-0 defeat to Hearts at Tynecastle.
And victory for John Brown's men at home to Aberdeen on Sunday will see the deficit trimmed further, with two games still to play.
But, asked if he truly believed his side could beat the drop after failing three times to secure the required win after meetings with Dundee, Hibernian and now Hearts, Lennon replied: "There's no doubt in my mind."
A win from either of their final two games - a home meeting with Aberdeen before a final-day clash at Kilmarnock's Rugby Park - will be enough to relegate Dundee, but Lennon did admit the erratic results posted by the Scottish Communities League Cup winners were self-inflicted.
He said: "In so many ways, we have progressed over the season. We've managed to win a national cup. We've gone up two or three rungs on the ladder, but in other ways we've gone back one or two.
"There's been an inconsistency there throughout the season and the league table doesn't lie. There is six very important points remaining and we want all six.
"Hopefully once we get our house in order we can find ourselves one or two places higher up the table."