The Buddies boss still believes his Paisley men can bridge a seven-point gap and steer themselves into the top half of the Clydesdale Bank Premier League for the first time.
Winning their game in hand over the rest of the SPL, therefore, would go a long way towards breaking new ground in the top-flight.
But John Brown's basement boys desperately need the three points too as they strive to complete the most unlikely of escape jobs by reigning in second-bottom Hearts, currently 15 points in front.
Brown was brought in as part of a last-ditch attempt to battle out of the drop zone and for that reason - along with the slim thread that currently holds his own team's ambitions in place - Lennon claims Wednesday night's Dens Park meeting will be a win-or-bust encounter.
The St Mirren manager - whose side are unbeaten in their two previous meetings with the Dark Blues this term - said: "I don't know Bomber (Brown) a great deal but you can see the impact that the change in manager has already had.
"They were unlucky to lose against Dundee United on Sunday in the Scottish Cup and fought back well against St Johnstone to get a draw last week.
"So we know it's going to be a tough game. Even though we have beaten them both times we have played them this season, they were hard games.
"But we are out to show our ambition and if we want to get to where we want to be then, it's a must-win situation.
"But likewise, if Dundee want to survive, they will need the three points too. Someone will ultimately end up disappointed."
The compact nature of the SPL table this season means just 16 points currently separate 10 of the 12 teams.
And for that reason, Lennon hasn't given up hope that his team - who sit in 10th place at present - could go even further than their original target of sixth.
He said: "This game is of huge importance to us because we still have a strong desire to keep chapping at the door for the top six.
"This is our game over all the other teams in the league and I believe we are still capable of fighting for three of the top six slots.
"Only Celtic, Motherwell and Inverness are guaranteed to be in the top six and the rest is up for grabs.
"There are plenty of twists and turns and a win would certainly keep us in there with a realistic shout.
"But it's totally down to us and we need to get the wins on the board."
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