"He was a strong-willed wee character, so it was just a wee bit sad."
Lambie's body was being kept in the freezer in case it could be used for research, she said.
"It would be a shame just to throw him down a hole - someone might benefit from it."
Ms Parker's three daughters Anna, 10, Sarah, 8, and Kate, 6, would play with the lamb.
"They were realistic that he wasn't meant to be, but we thought he may have got through the worst of it because he'd been tailed and he was feeding off the lamb feeder."
The family was "pretty lucky" to be involved with such a special lamb, Ms Parker said.
Lambie had two faces and four eyes, two of which appeared to have merged in the middle and did not blink.
When his left eye blinked, so did the right. When he cried, the other mouth opened too.
After the lamb's birth, Ms Parker told the Herald: "The lamb actually fell in the creek. I rescued it and went to put it back with its mother.
"I thought, 'Oh, the back of his head looks a bit strange'. And I turned it round and wow. I just thought, 'Heck, what's this'?"
The family had heard of other lambs being born with a similar deformity at nearby farms, but none had survived longer than a day.
Ms Parker had said in September: "He interacts with the other lambs and he wags his tail and talks to you.
"The kids and I know that he's not going to live for long...but we're giving him a chance just like any other lamb."
