The Swede, who has also made her first cut on tour in Amsterdam this week, got off to a flying start with birdies on the first, second and fourth to move to 10 under for the tournament.
But consecutive bogeys on the sixth and seventh and one more on 17 saw the 24-year-old slip back to seven under, one ahead of England's Holly Clyburn.
Despite missing four cuts this season, Lennarth does have a second-placed finish at the South African Open under her belt after the tournament was abandoned after one round due to high winds.
Clyburn, who started on the 10th on Saturday, is also in her maiden season on Tour and she carded a blemish-free 69 with birdies on the 10th, 16th, first and eighth.
Fellow Englishwoman Melissa Reid was a further two shots back after adding a 72 to Friday's 70 and sat in a group with Spain's Carlota Ciganda and home-favourite Christel Boeljon.
Spain's Tania Elosegui was three under after firing a 69, the joint best round of the day with Clyburn, with Scotland's Pamela Pretswell, Swede Carin Koch and Germany's Miriam Nagl.
There was then a large group of players on one-under par including 17-year-old Englishwoman Charley Hull.