The animals suffered heart attacks and died after the incidents over two weekends in the Battleford Road area.
Police said the lambs died as a result of "animal cruelty".
The lambs belonged to Roberta McMullan who said she felt sick that somebody would do "the like of that on a defenceless animal".
"Why? I can't understand it," she said.
"You know each one of them personally nearly and it's just horrendous when you go out to find something like that."
Ms McMullan  has about 50 pedigree Suffolk sheep.
"It's bad enough when you go out to find them dead due to an illness, but to find out that... words cannot express it really," she said.
The police said they had increased patrols in the area and have appealed for information.
President of the Ulster Farmers Union Ian Marshall said they were deeply concerned about such attacks.
"It is sickening to think that someone could feel justified to carry out this sort of an act against lambs," he said.
An Armagh farmer has described an attack on her lambs in which their right ears were cut off as "horrendous".