A quartet of Australians - Peter Fowler, Marcus Fraser, Wade Ormsby and Nick O'Hern - are among eight players tied for fourth place at 4-under-par 68. They were joined there by Marten Olander, Peter Hedblom, 2003 British Open champion Ben Curtis and Andrew Oldcorn, the 2001 winner of this event.
The Irishman dropped a shot on the seventh with a three-putt bogey, but holed a sand-wedge from 124 yards out for eagle at the par-4 eighth to jump to minus-3.
The 31-year-old faltered to another bogey at the ninth. Lawrie slid back to 1-under after a bogey on No. 11 but he caught fire down the stretch.
Lawrie rolled in a 6-foot birdie attempt on the par-4 13th. He chipped in for birdie from just over the 14th green and capped a run of three straight birdies as his birdie putt on 15 dropped into the cup. He closed with a 4-foot birdie putt at the last to grab a share of the lead.
'It was a great draw to be off first this morning. The greens were in perfect condition,' said Lawrie. 'You've got to take advantage of it and that's what I did today. I played lovely.'
McDowell tripped to a bogey on the second, but atoned for that error with a birdie on the next. The Ulsterman then holed an eagle on the par-5 fourth but fell back to even-par after bogeys on six and nine.
Around the turn, the two-time champion on the European Tour moved back to minus-two with birdies on 11 and 13. McDowell ran off three consecutive birdies from the 16th to climb to minus-5.
'I am pretty content with that finish,' McDowell said. 'It's always nice to finish well. I played solid. I'm surprised that it wasn't a little better than it is. I'm pretty happy to be in at 5 under. That's something to build on.'
Lima stumbled out of the gate with a bogey at the first. He picked up a birdie at the fifth, but struggled to a three-putt bogey at the sixth. The 23-year- old recovered with back-to-back birdies from the seventh.
He two-putted for birdie on the 12th. Lima made it two in a row as he birdied the par-4 13th and got to minus-4 with a birdie on the 16th. Lima, like his fellow leaders, birdied the par-5 closing hole to finish at 5 under.
'That was a strange round, because I woke up this morning with a big pain in my back, but the physio guys did good work on it,' said Lima. 'I had just a little pain on the course, but everything is going perfect now.'
Australian Peter Lonard carded a 3-under-par 69. He was joined in a tie for 12th place by Steven O'Hara, Robert Coles, Stephen Dodd, Alastair Forsyth, Peter Hanson, Brad Kennedy and Damien McGrane.
Nick Faldo, a four-time winner of this event, is one stroke further back at minus-2. Among others also at minus-2 are U.S. Open champion Retief Goosen, Padraig Harrington and Miguel Angel Jimenez. Defending champion Scott Drummond finished at 1-under-par 71 while World No. 3 Ernie Els managed a 73 in the opening round.