Kjeldsen and Lawrie both had seven birdies and two bogeys around the Parador Golf Course on the Costa Del Sol. They each shot 30 on the front nine.
Seven players were a stroke behind.
Ranked 35th at the start of the year, Kjeldsen has secured a place to play in the Masters next month. But he has slipped to 51st and failed to join many fellow Europeans warming up at Bay Hill this week for the first major of the year.
"I would have like to have played Bay Hill, but at the same time I also wanted to defend the Andalucian Open title," Kjeldsen said. "In the end, if you are playing well in the buildup to a major it doesn't matter whether you do it in Spain or America."