Two Face has double of everything and has four eyes; two of which appear to have merged in the middle and do not blink.
When his left eye blinks, so does the right. When he cries, the other mouth opens too.
And when he drinks milk from the left side, the tongue on his right side moves also.
"It's almost like he's got a mirror down the middle," Ms Parker said.
The farmers had heard of other cases of lambs born with a similar deformity at nearby farms, but none of them had survived past a day of being born.
Ms Parker said her three young daughters - Anna, 10, and Sarah, 8, Parker and Kate Wilson, 6 - were smitten with their new "lambie" and loved to feed and cuddle him.
Ms Parker said Two Face was, apart from his deformity, a normal animal.
"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."
Next trending article: Inside the $1 million Grey Lynn hovel