The lamb was found by a mother and daughter out walking at Lurgybrack on the outskirts of Letterkenny.
The lamb was put in a cold storage facility at the DSPCA centre in Letterkenny.
DSPCA officer Kevin McGinley said he did not know about the incident involving the lamb for a number of days after the incident.
Mr McGinley said that a clinical autopsy on the lamb would have to be carried out in Sligo.
A general autopsy could be carried out locally but the evidence of the death could not be used in a court.
Mr McGinley said it is doubtful if it will ever be discovered what happened to the lamb.
“I am told that there was no obvious marks on the lamb. I don’t think we will ever know what happened to it.
“It can be sent to the Sligo laboratory if Gardai make that request but I’m not even sure if the Gardai are involved,” he added.