In the first match, Cumberland, having won the toss, posted a competitive total of 153 for 3, principally due to a third-wicket stand of 121 by Jacques du Toit (73) and captain Gary Pratt (53 not out).
Alex Willerton with 2 for 29 was Lincolnshire’s most successful bowler.
Lincolnshire’s reply began in steady fashion and after 10 overs they were 47 for 2.
The tempo increased after this but when Louis Kimber was dismissed for 65 the sixth wicket had fallen at 108.
From thereon Lincolnshire were always behind the required run rate and finished on 131 for 9, Cumberland winning by 22 runs.
Du Toit completed a fine all-round performance with 5 for 20 from his four overs.
In the second match Cumberland again won the toss and batted first, and whilst losing wickets steadily throughout their innings reached a total of 139 for 7.
Du Toit was again their top scorer with 38 and for Lincolnshire Alex Willerton, with 3 for 15, was their most successful bowler.
Lincolnshire’s reply suffered from the loss of two early wickets and again they fell behind the required run rate.
Bilal Shafayat with 60 not out and Harry Warwick with 30 raised hopes for a close finish but it was not to be, Lincolnshire closing on 121 for 5, Cumberland winning by 18 runs.
Lincolnshire would now need to win all their remaining matches to stand a chance of finals day qualification.
They next meet Staffordshire on Sunday, at Rolleston-on-Dove.