The lowly Rapids were stifled by spin as they posted only 127 for eight on a pitch used for a Women's Super League game earlier in the day.
Lancashire's quartet of spinners returned four for 66 from 13 overs combined, with an in-form Matt Parkinson the pick of them with one for 14 from four.
Jos Buttler and Liam Livingstone then shared a third-wicket stand of 76 in 11 overs.
Livingstone hit 36 off 37 balls without a boundary, while Buttler finished unbeaten on 52 off 40 with four fours and two sixes.
The Lightning, with 13 points from as many games, move up a place to sixth with their fifth victory. They host Birmingham on Friday and must win and hope other results go their way to qualify.
They are currently 14/1 with Sky Bet to win the Blast, with Nottinghamshire 100/30 favourites followed by Glamorgan at 6/1.
Parkinson's economy rate was much talked about even before this game having returned four for 23 in the defeat to Yorkshire last Friday.
Here, he bowled Daryl Mitchell with a big-spinning leg break in his latest miserly spell.
Of all bowlers who have bowled more than three overs in this season's Blast, the 20-year-old's economy rate of 5.78 runs per over is the best. He has 13 wickets from eight appearances.
Off-spinner Arron Lilley struck twice and later hit a brisk 31. Left-armer Stephen Parry opened the bowling and struck in the seventh over to get Mitchell Santner caught at deep mid-wicket.
Pakistan overseas seamer Junaid Khan also claimed two-for.
Only captain and opener Joe Leach, who fell to a brilliant one-handed diving catch by Buttler off Ryan McLaren, and Brett D'Oliveira made it into the twenties for the Rapids with 24 off 17 balls and 30 off 33 respectively.
Josh Tongue got rid of Jordan Clark courtesy of a fine tumbling catch at short fine leg by debutant Patrick Brown, four balls into the Lightning chase.
Lilley then hit three fours in a row off Tongue at the start of the fifth over to take his side to 34 for one and ahead on the Duckworth-Lewis method, with rain threatening the Manchester area.
He had hit five fours by the time he was trapped lbw by leg-spinner D'Oliveira as the score fell to 47 for two in the seventh.
Livingstone and Buttler took the score to 68 for two after 10, and when the latter hit Alex Hepburn's medium pacers for six over long-on to take the score to 90 for two in the 14th, it was the first boundary in almost eight overs.
The half-century stand came up off 45 balls in the next over before, with net run-rate in mind, the last 30 runs came in double-quick time for the loss of only Livingstone.
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