The England Twenty20 international struck nine fours and a six from just 41 balls which ensured that Nottinghamshire, who were set a revised target of 194 from 30 overs, were well ahead of the rate when it was further adjusted to 133 in 21 overs after another stoppage for rain.
Nottinghamshire needed 21 from 20 balls when the players returned but they eased home with nine deliveries to spare thanks to a composed unbeaten 39 from James Taylor.
Warwickshire's total of 186 for seven, based around Rikki Clarke's first one-day half century in a year, looked competitive - but Lumb soon made it look inadequate as he contributed 43 to an opening stand of 52 with a subdued Alex Hales.
Lumb was quickly into his stride, taking three fours from Chris Woakes' opening over then straight driving Chris Wright for a six. Woakes and Wright both absorbed heavy punishment so Warwickshire turned to New Zealand off-spinner Jeetan Patel who struck with his first ball when Hales shovelled a catch to Ateeq Javid at square leg.
Lumb raced to a 28-ball half century but then failed to dig out a yorker from Steffan Piolet's first ball. Samit Patel holed out to deep square in Boyd Rankin's first over just before umpires Neil Bainton and Steve O'Shaughnessy took the players off for rain but Taylor finished the job that Lumb had started.
Warwickshire managed only 29 in their opening eight over power play and, thanks to Lumb's superb strokeplay, Nottinghamshire needed only 18 balls to pass that figure.
Warwickshire's innings was twice interrupted early on by hailstorms which meant that the match was reduced first to a 37 overs contest and then to 30 overs after a second and more lengthy stoppage.
Warwickshire stuttered as Varun Chopra struggled to time the ball but Clarke got the innings going after he was promoted up the order by lifting Patel for six over long on. Chopra grafted for his 42 before he went leg before wicket sweeping Steve Mullaney but Clarke was more fluent and reached a 42-ball 50 in the penultimate over of the innings.
Clarke, who was bowled pulling Jake Ball, was given spirited support by Tim Ambrose and Piolet, who provided late acceleration with unselfish cameos, but Warwickshire were still left seeking their first win in this season's competition.