Sweden's Robert Karlsson was one shot further back after a 3-under 69. He was joined by Greg Owen of England at 9-under-par 207.
Bjorn, who has responded well to the disaster he experience in the final round of last week's British Open, was four shots behind Lynn to start the third round at Portmarnock Golf Club and collected five birdies and one bogey over his first nine holes to make the turn at 10-under.
'I could win the next three events and it wouldn't make up for it,' Bjorn said of his negative memories of Royal St. George's. 'Nothing will make up for last week until - if - I win a major championship. The only thing it would mean to me is that I am doing the right thing and I can go out on this tour and still be a force to be reckoned with.'
The Dane reached minus-11 with a birdie at the 13th but stumbled with back-to- back bogeys starting at the 12th. Bjorn recovered with a birdie at the 16th only to drop another shot with a bogey at the 17th.
Bjorn then birdied the par-4 18th to assure himself of a share of the 54- hole lead.
Campbell, who finds himself in contention for the first time this season, jumped out of the gate with two straight birdies from the first to move quickly to 11-under.
The New Zealander struggled with three bogeys over his next 10 holes but countered with a birdie at the 13th. Campbell then birdied the 16th en route to a round of 71.
'Winning would mean a huge weight lifted off my shoulders and the reassurance that I can be a winner on the European Tour again,' said Campbell. 'I never doubted I could get back into this position. Never.'
Lynn, who held the outright lead after 36 holes, faltered early with a bogey at the second. He went out in 37 before notching his first birdie of the day at the 10th.
The Englishman bogeyed the 11th but responded with a birdie at the 13th. Lynn found trouble again with a bogey at the 14th, but regained the shot with a birdie at the par-3 15th.
'I have been in the last couple of groups five times this year so that is pretty good,' said Lynn, who managed a 72 in the third round. 'It gets the juices going a bit and it's just a case of being patient. You can't force things under these circumstances.'
Peter Lonard of Australia shot a 69 to finish alone in sixth at 8-under-par 208. Ireland's Peter Lawrie and Peter Hedblom of Sweden were one shot further back at 7-under-par 209.
Jean-Francois Lucquin, Ben Mason, Ian Poulter and Shaun P. Webster share ninth place at 6-under-par 210.