Cheshire won the toss and elected to bat.
Lincolnshire immediately took a firm grip on the game with Alex Willerton leading the attack in devastating fashion.
No Cheshire batsman reached 2 runs and in 22.5 overs they were dismissed for 88, Willerton taking 6 for 20 in his 10 overs.
This made him Lincolnshire’s leading all-time wicket taker in one-day cricket with his figures of 6 for 20 being the best ever for the County in the competition.
Lincolnshire lost two early wickets before rain delays interrupted their progress.
As a result, they were set a revised target of 80 from 34 overs.
This they reached for the loss of four wickets, Bilal Shafayat with 39 not out and Tom Keast with 25 paving the way to victory in 16.4 overs.
Lincolnshire will now meet Cumberland in the quarter-final at Bourne on Sunday, June 30 (11am start).
Lincolnshire’s next match is at Scunthorpe CC on Sunday, June 9 (11am) when they play Staffordshire in two T20 matches.
Lincolnshire currently lead their group in this competition having won all four of their matches so far.