A trio of half-centuries for Mark Cosgrove, Cameron Delport and Mark Pettini proved key for the Foxes against a Lightning side including England Test duo Jimmy Anderson and Haseeb Hameed.
But an unbeaten 32 for Tom Wells saw them over the line with four balls left in this North Group opener.
Hameed hit a composed 88 on his senior limited overs debut as Lancashire looked well placed with a total of 314 for eight having elected to bat.
But the hosts will be frustrated at not taking full advantage of being ideally placed at 173 for two after 32 overs.
Leicestershire recovered from losing three for 18 in 3.1 overs to slip to 244 for six shortly after a near 20-minute rain delay, and they later secured 49 needed off the last six overs.
Left-arm spinner Jamie Sykes claimed career best figures of four for 57 from his 10 overs, including three of six wickets to fall in the last 18 overs of Lancashire’s innings.
Hameed shared stands of 81 for the first wicket with Alex Davies (41) and 73 for the third with captain Liam Livingstone (39).
Livingstone later took two wickets in an over with his off-spinners and completed a brilliant sprawling catch running back towards the long-on fence to help Anderson get rid of Delport for 62.
At that stage, it looked like being a key intervention as the Foxes fell from 101 without loss to 137 for three in the 26th over.
But Cosgrove and Ned Eckersley (39) shared a brutal fourth-wicket stand of 89 in 12 overs.
They made sure their side were ahead of the DLS par score when rain took the players off at 8.20pm with the score at 218 for three in the 37th.
The target was then revised to 309 off 49 overs.
Pettini and Delport shared 101 inside 18 overs for the first wicket, with each hitting a six in scores of 59 and 62.
Livingstone then had Pettini lbw and Neil Dexter caught at mid-on over in the space of three balls before taking his stunner of a catch to remove left-handed South African Delport.
Hameed, who hit nine fours in 101 balls, looked good on the drive and down the ground on the way to his first half-century since December whilst on England’s Test tour of India.
He was the second of Sykes’s wickets.
The 25-year-old had opener Alex Davies caught at backward point reverse sweeping for 41 before getting Hameed caught behind down leg, Dane Vilas caught at deep cover and Ryan McLaren at long-on.
Cosgrove was Leicestershire’s standout with the bat with 67.
He had a running battle with a fired up Anderson, but the Australian struck the ball cleanly.
The left-hander was one of the three quick wickets to fall, but his departure did not prove costly.