The 1999 British Open champion was beaten one up by fellow Scot Chris Doak who will now meet former Ryder Cup player David Howell of England in the last 16.
"I hit it really, really poorly and you can't get away with hitting the ball as poorly as that," Lawrie told reporters. "You can't hit the ball any worse than that.
"The two of us didn't play very well and were all over the place at times. I am disappointed, gutted, to be knocked out but when you play like that at this level you seldom get away with it."
Doak is joined in round three by countrymen Richie Ramsay and Marc Warren, former European number one Robert Karlsson and his fellow Swede Johan Carlsson, and Belgian Nicolas Colsaerts.
Also through are English pair Tyrrell Hatton and Chris Wood, Frenchmen Julien Quesne and Gregory Havret, Northern Irishman Michael Hoey, Dane Morten Orum Madsen, American Peter Uihlein, Thailand's Kiradech Aphibarnrat and Thomas Aiken of South Africa.
(Writing by Tony Jimenez, editing by Ed Osmond)
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