And Anderson believes that if the Kieswetter-Lumb partnership comes good, they will have a "great chance".
In the end, bad light had the final word but once Lumb and 18-year-old James Vince had taken 17 off the sixth over, bowled by Ben Harmison, they were always well ahead of the required rate.
South African-born Lumb, 29, joined Hants from Yorkshire for the 2007 season and impressed in scoring 76 in the FP Trophy semi-final victory against Lancashire.
The in-form Michael Lumb and Pothas threatened a recovery, only for Mitch Claydon to dismiss Lumb and Liam Dawson with successive deliveries.
Fielding at mid-on to the right-handed Kieswetter, and mid-off to the left-handed Michael Lumb, he proceeded to drop three catches in the first five overs, only one of which was at all difficult.
In the Friends Provident Trophy, Pro 40 and Twenty20 combined, the impressively consistent Lumb has now hit 985 limited-over runs this summer, including two centuries and nine fifties in 24 innings.
The negative factor for England was clearly the top-order batting, Lumb having registered a second failure and Pietersen out first ball after replacing Ravi Bopara, having missed the Bangladesh game to be with his pregnant wife.
Left-arm seamer Wahab Riaz gave Pakistan hope when he dismissed opener Steve Davies (14) and Michael Lumb in successive deliveries as the Lions stuttered at 34-2 in the fourth over.
Needing to win at Trent Bridge in their final group game to guarantee qualification, Dominic Cork's 4-18 helped blow Notts away for just 145 before Michael Lumb and Jimmy Adams shared an unbroken opening stand to lead Hampshire to a 10-wicket win and a guaranteed home quarter-final.
England's openers did get lucky on occasion - umpire Simon Taufel rejected a perfectly good lbw appeal by Mathews against Kieswetter when the right-hander had made 16, while Lumb only avoided being run out on 11 when Ajantha Mendis made an embarrassing mess of taking Lasith Malinga's return.
Michael Lumb contributed 76 to the Hampshire total as Charl Willoughby claimed 3-69.
Ajmal redeemed himself when he had Lumb stumped in his first over, before Kieswetter was caught at long-on off Abdul Razzaq two overs after driving Mohammad Hafeez for an enormous six which took a chunk of masonry out of the Sir Garfield Sobers pavilion.
The Hampshire innings did not get off to the best start when new signing Michael Lumb fell in the third over with the score on 18 but the big-hitting middle order pair dominated the Irish attack.
BBC: SPORT | Cricket | Counties | Pietersen steers Hampshire home
Hogg trapped Lumb lbw and Keedy removed Carberry and Benham to leave the visitors wobbling on 71-4.
Lumb followed his 219 in the County Championship last week with an unbeaten 57 out of 87-1 in 11 overs, well ahead of schedule when bad light ended play.
Lumb should also have been caught on 23 by substitute fielder Nuwan Kulasekara, running in from long-off, in the ninth over.
But Lehmann and Michael Lumb (98) did share a club record fourth wicket stand of 358 before they declared on 677-7.
BBC: SPORT | Cricket | Counties | Lehmann marathon lifts Yorkshire
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