Lennon led the club to League Cup glory last term, but he has made climbing the table his primary goal as Buddies boss.
He has twice seen the Paisley side scrape home in 11th, but did hand the club their best top-flight finish in 20 years when he took them to eighth the season before last.
But a home win against Scottish Premiership basment boys Hearts on Sunday combined with defeats for Hibernian and St Johnstone will put Saints on the verge of a place in the top half of the table for the first time this season.
Now the former Cowdenbeath boss says his side's chances of finally claiming place in the top six come the end-of-season split have never been better.
Lennon told Press Association Sport: "With the group of players we have this year, there is no doubt that is the case. Over the last 14 games, you can see we are getting there.
"If we could get into the top six, it would be another level of progression for this club. It's hung over St Mirren for a generation, but we have always ended up flirting at the wrong end of the table.
"There is a long way to go, but if we can keep picking up points it will fuel those ambitions."
Hearts defender Kevin McHattie says he is hoping 2014 will be a successful year on and off the pitch for the troubled club.
The Tynecastle outfit face St Mirren in the Scottish Premiership on Sunday in their last game of what has been a fraught calendar year.
Hearts plunged into administration in June with debts of nearly £29million.
The young team have also struggled in the Premiership this season after the club were hit with a 15-point penalty and were handed two separate transfer embargoes.
Hearts are 14 points adrift at the basement but McHattie is desperate to help spark a turn around in their fortunes.
He said: "Am I glad to see the back of 2013? In some ways yes, but with everything the club has been through, and all the fans sticking by us, it's been a great year in that way."
McHattie has been heartened by the way the fans have stuck behind the players in the face of adversity.
"Hearts is a massive family club. The supporters have always been there for us, so we'll try our best to pay them back for that.
"On the pitch it's obviously been disappointing for us, but we'll try to change that in 2014."
McHattie is hopeful the club can see improved fortunes both on and off the filed in 2014.
"Hopefully we come out of administration and have a brighter future, starting on Sunday.
"We've just got to do what we can. Just work hard - that's all we can do, really."
Hearts manager Gary Locke's squad is still stretched to the limit ahead of the clash at St Mirren Park.
Locke could only name six substitutes for the Boxing Day defeat by Kilmarnock with Gary Oliver (ankle), Ryan Stevenson (hamstring), Mark Ridgers (knee) and Jason Holt (foot) all out.
Danny Wilson has been playing despite a shin splints problem and will need to play through the pain barrier again.