The club's last top-half finish came in 1985 and with only eight games before the SPL split, Lennon is keen to end their long wait.
Ahead of Saturday's meeting with Motherwell at New St Mirren Park, Lennon's side are currently two points behind sixth-placed Aberdeen.
"A whole generation of St Mirren fans have not seen their team in the top half of the league and that's very much on our minds," said Lennon.
"We are about to come into a period of games that will define our season, we are only two points off a top-six spot and it's going to be a race between four teams to get that place. We know it will come down to who can hit the best form.
"It would be fantastic for the club to achieve a top-six place and clinch our highest position in 27 years.
"We have a very young squad here and we will need the older heads to breed that winning mentality."
St Mirren will be without Hugh Murray for Saturday's clash with Stuart McCall's Motherwell after the defender was ruled out for a month with a calf injury.
Saints are yet to get the better of the Fir Park side this season and Lennon is hoping for a change in their fortunes.
"The two matches between the clubs have been thoroughly entertaining and closely fought games," he said.
"Hats off to Stuart McCall and his staff, they have firmly established themselves in third place in the table and achieved good levels of consistency.
"Their recent away form hasn't been great recently though and hopefully on Saturday we can continue that by taking all three points."
Despite remaining very much in the race for a place in the upper reaches of the SPL, St Mirren are yet to record a league victory this year.
Lennon believes his team must show a ruthless streak as they aim to turn draws into victories.
"There is a fine line between winning and losing and even winning and drawing," Lennon added.
"We have had to lion's share of possession in a majority of our matches this season but haven't always been able to make that count.
"It is important that we find a more ruthless streak in front of goal and try to turn the games we are only managing to draw into wins."
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