And Anderson believes that if the Kieswetter-Lumb partnership comes good, they will have a "great chance".
Michael Lumb added a calm 81 as Lehmann dominated an unbroken stand of 299.
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Hogg trapped Lumb lbw and Keedy removed Carberry and Benham to leave the visitors wobbling on 71-4.
Lumb was playing particularly well, and both batsmen piled into the fourth over, taking 19 runs off Mohammad Asif.
Michael Lumb and Joe Denly are the only uncapped players in the squad.
All three wickets had fallen to Jamie Squires but Wagh then made his impact, bowling Michael Lumb for eleven.
Michael Lumb contributed 76 to the Hampshire total as Charl Willoughby claimed 3-69.
Michael Lumb and Kevin Pietersen had fallen in the first over to Rory Kleinveldt before Craig Kieswetter departed to Morne Morkel's second ball.
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
Paul then removed Scott Newman in the first over of England A's second innings, before Michael Lumb fell lbw for 13.
Lumb should also have been caught on 23 by substitute fielder Nuwan Kulasekara, running in from long-off, in the ninth over.
Michael Lumb and Craig Kieswetter are clean and powerful hitters who easily clear the inner fielding circle in the first six overs.
The in-form Michael Lumb and Pothas threatened a recovery, only for Mitch Claydon to dismiss Lumb and Liam Dawson with successive deliveries.
Craig Kieswetter and Michael Lumb then put on 68 in 8.1 overs for the first wicket to put England firmly on course.
Michael Lumb and Chris Benham fell cheaply, but Ervine and Pothas steadied the innings as Kent looked to press their advantage home.
Meanwhile, Yorkshire believe they can still convince batsman Michael Lumb to stay at Headingley amid speculation linking him with a move to Hampshire.
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Craig Kieswetter and Michael Lumb have proved an inspired opening combination, with Kevin Pietersen and Eoin Morgan both in imperious form in the middle order.
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.
Lumb was trapped leg before, while Dawson had his stumps rearranged.
Hampshire started badly when Chapple struck to remove opener Jimmy Adams for just nine before Michael Carberry and Michael Lumb moved the score on to 50.
There is a balance between absurdly giving your wicket away and falling in the team cause, and it is something Kieswetter and Lumb should think about.
Surrey tried hard for further success in the closing overs but Adams refused to budge as he and Michael Lumb (15) saw it through to stumps.
BBC: SPORT | Cricket | Counties | Surrey spin pair unsettle Hants
Hampshire's sizeable task took on herculean proportions as Gibson found the edge of Michael Lumb and Ervine's bat and Di Venuto held on at second slip.
Kieswetter, who made his debut on the recent tour of Bangladesh, will team up with Lumb for the first time at senior international level in the Caribbean.
"The two guys at the top of the order, Kieswetter and Lumb, are still going at the bowlers and again got us into a good position, " Collingwood added.
On a slow pitch, Rayner then got going by bowling Michael Lumb as he played back before he had John Crawley taken at slip, nibbling at his arm ball.
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.
But Vince struck the ball very cleanly in his 22 not out, while Lumb reached his 50 with his only six, cleanly struck over extra cover off Will Gidman.
Australian Darren Lehmann collected six boundaries in his 37 off 39 balls before he was run out, but Michael Lumb (27) and White (17) prevented further damage before the interval.
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