Thunder slipped to 33-4 inside six overs as openers Eve Jones and Darcey Carter, plus captain Ellie Threlkeld, were all caught trying to clear the inner ring, while Seren Smale was stumped.
New-ball seamers Grace Ballinger and Charley Phillips removed Jones and Carter before the off-spin of Australian overseas all-rounder Charli Knott accounted for Smale and Threlkeld in the space of three balls in the sixth over.
But overseas star Lanning set the ball rolling on a recovery, first in partnership with Fi Morris and then Lister.
Lanning shared 29 for the fifth with Morris, who fell caught at short third for 14, off a top-edged pull at Ballinger, and then added 100 in 9.5 overs with Scottish international Lister.
The sixth-wicket pair shared four sixes. Lanning hit three of them all around the wicket in the last two overs, which cost 33 combined.
One was slog-swept off Kathryn Bryce’s seam in the penultimate over, the other two hit over long-off and midwicket against Phillips in the last.
The Blaze lost Marie Kelly to Grace Potts early in their chase, but Beaumont hoisted Tara Norris for two sixes over midwicket and long-on in the third over to get things moving
She then slog-swept her former England team-mate Kate Cross for a third six and was punishing as the home bowlers struggled to find a consistent length.
Beaumont reached her fifty off 24 balls just outside the powerplay, but then came Thunder’s second recovery as spin prospered.
She was bowled pulling at Carter’s off-spin before Kathryn Bryce dragged a Morris full toss to long-on.
Georgia Elwiss was bowled by the left-arm spin of Hannah Jones, following two deflections off body and bat as she aimed to sweep, and Knott skewed the same bowler to backward point, leaving Blaze five down and 63 short of victory.
Emma Jones also holed out to long-off against Morris (3-25), but Scotland international Bryce was helped along by captain Kirstie Gordon, who contributed 20 to a 45-run seventh-wicket stand.
Bryce was caught behind off Potts with the first ball of the last over and four still needed, but it was too little, too late for Lancashire.
Match report supplied by ECB Reporters’ Network, supported by Rothesay.