The hosts won the toss and chose to bat in Manchester, but their innings got off to a nightmare start when Ashwell Prince (1) was caught by Michael Lumb off the bowling of Samit Patel in the very first over.
Paul Horton (1) soon followed his fellow opener into the pavilion to leave Lancashire on 4-2, while Alex Davies was run out by Sam Wood without even facing a ball to hand the visitors their third wicket in as many overs.
Croft also reached 51 and was there at the end with James Faulkner (32) as the Lightning salvaged a total of 137-4 following their inauspicious start.
The Outlaws began better than their opponents, losing only Lumb (11) in their opening 10 overs, but the wickets started to tumble more regularly after Riki Wessels was dismissed for 28.
James Taylor remained defiant at the crease and sent Notts into the final over with a chance of victory, and they reached the last ball needing just one for a draw. However, Taylor stroked a four to the boundary to seal a dramatic victory and keep alive his side's hopes of reaching the knockout phase.