The 24-year-old from Stockholm posted a seven-under-par 66, her first sub-70 round in what has been a difficult start to life on the Ladies European Tour.
But barring a dramatic reversal in fortunes in the second round she will make a cut for the first time.
Bizarrely, she has a joint second-placed finish behind her, but that came at the tour's South African Open when play was abandoned after one round due to dangerously high winds. She carded a 70 there, and picked up a cheque worth over £12,500.
This time Lennarth will be hoping for a full weekend of play, having begun in such rich form. Starting on the back nine, she had four birdies in her opening seven holes, and the finish with a flourish capped a successful day.
She said: "Before I teed off I saw the leaders at three under and I was a little surprised. I just aimed for a par on every hole and things went my way. I made some putts and that gave me some momentum."
Having finished sixth in the tour's qualifying school, Lennarth began the year full of optimism, however four missed cuts from five tournaments - the South Africa event being the exception - have shown her how tough it can be.
The former University of Alabama student said on the tour website: "I was hoping for a better start this year, I played well at Q-School but I've been struggling so it's nice that even though I didn't strike the ball as well as I can, I got a great score out there. This is the best score I've ever posted in a tournament."
Sharing second place on four under were France's Gwladys Nocera and Norwegian Benedikte Grotvedt, with both returning scores of four-under 69, while England's Melissa Reid was the best-placed Briton on three-under 70.
Reid set out on a bitter morning, and said: "It was so cold this morning that you couldn't warm up and you were shivering putting your ball on the tee so the mental side was to get over that. When you're freezing you have to keep your body warm and your hands warm and that's the biggest challenge."