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 their 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 - told Press Association Sport: "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."
- Sports & Recreation
- Clydesdale Bank Premier League