Pressel posted a 6-under-par 66 midway through the first day's play for the clubhouse lead. A few times a player would pull into a tie with Pressel but none stayed there until Lennarth's final-hole birdie.
Lennarth, who was an LPGA rookie last year, was bogey-free on her round with three birdies on each side for the 66.
Pressel, who won her first LPGA title at the 2007 Kraft Nabisco Championship but has one title since then -- and none since October 2008 -- took the lead with three consecutive birdies over Nos. 13-15 at The Old Course in St. Andrews, Scotland.
Seven players are tied for third place one stroke behind the leaders and another seven are two strokes behind.
The group at 5-under includes world No. 2-ranked Stacy Lewis.
Inbee Park, the world No. 1 who is seeking a record fourth major title this year, is among a crowd of 21 at 3-under 69.
Park was 6-under through 10 holes but had a bogey at the 13th hole. She then posted a double-bogey 6 at the 16th and a bogey at 17 before closing the day with her seventh birdie.
Swim Week Miami Beach 2014 [PHOTOS]