Remains of 11 American signal crayfish have been discovered near Tebay.
The species carries crayfish plague, a "devastating" fungal disease that has "significantly threatened" the native population in the south, the EA said.
Judith Bennett, from the agency, said it can "wipe out a native population" which has no natural resistance.
The crayfish were found in a river in the Lune Valley.
"Fortunately, in this instance, it appears that the signal crayfish were already dead when they were dumped in to the river," Ms Bennett said.
"We remain concerned that someone may have tried to release live signals into the water, which could be potentially devastating."
Two recent outbreaks of crayfish plague have been identified in Yorkshire and Devon.
It is an offence to release American signal crayfish into the wild or to trap or kill native crayfish.
An invasive species of crayfish found dumped in a Cumbrian river is a "major concern" for the native species, the Environment Agency has said.