Showers struck at the Blackpool ground severely curtailing play.
With the outfield conditions difficult and amid long spells of rain, Derbyshire reached 132 for two in the 22nd over when the umpires decided that play could not continue.
By that point the match had already been reduced to 36 overs per side.
The rain meant a further reduction in the number of overs if play could continue.
The rain finally stopped and a mopping-up operation by the ground staff got under way
Before the interruption, Derbyshire opener Ben Slater was unbeaten on 60.
Skipper Billy Godleman was caught by Ryan McLaren off the bowling of Jordan Clark for 20.
The second wicket to fall was that of Shiv Thakor caught at the wicket by Alex Davies for 38.
Thakor had been particularly punishing of Jimmy Anderson in the previous owner, including hitting him out of the ground for a sweetly-struck six.
Under the Duckworth-Lewis system, Lancashire were set a revised target of 161 in 18 overs, the Derbyshire innings having been closed.