Lawrie, who had five birdies, was playing on the Golf du Palais Royal course. The field was split into two, with Bickerton on the Golf de L'Ocean course.
Lawrie, whose only previous European Tour win came three years ago, is three shots ahead of defending champion Rhys Davies of Wales and Shiv Kapur of India. Both joined Lawrie on the Golf du Palais Royal.
"I got off to a great start with an eagle at the 10th hole. ... I holed out from about 25 feet," Lawrie said. "After that I played lovely, gave myself lots of chances and made one stupid bogey where I missed the green left on the third."
Davies, defending his first title as a professional, had six birdies and a bogey in his round of 67, while Kapur had five birdies and one eagle.
The 41-year-old Bickerton said he struggled with the heat.
"It was a very tough day in that respect, especially when you look at the length of the rounds we were playing," he said. "I am a player who will always try and help my amateur partners too, so there was a lot of concentration used up out there today because we were out there for almost six hours."
Lawrie conceded the players on his course had an easier time than Bickerton and others on the Golf de L'Ocean.
"I think we got very lucky with the draw, to be honest," Lawrie said. "The wind calmed down on the back nine, and the front nine, the windier nine, was when the wind was dying down a lot."
Davies was encouraged by his opening round, after failing to finish in the top 20 so far this season.
"I hit the ball a lot better than I have been lately," Davies said. "I was able to put the ball in the right position on the greens, which is important out there, and I was able to roll some putts in at key moments."