Their son, Greg Lee, was initially employed as the company workshop manager in 1985 but eventually took control of the company in the 1990s.
He bought the shares for $200,000 in 2000.
His two siblings Robert Lee and Helen Heard have since challenged the transfer.
The court documents stated the pair claim Greg Lee: "improperly benefited from those transactions, which he procured by exercising undue influence over their parents and in breach of fiduciary duties. In doing so, he gained an unconscionable bargain."
The documents said the pair argued "During the period from 1994 until their death, Ray and Joyce's health and mental capacity deteriorated significantly" including "consuming excessive amounts of alcohol".
Joy Lee was diagnosed with bipolar mood disorder and alcohol abuse in 1994 before having a mini stroke and a heart attack in the late 90s, the court documents said.
In early 2000, Ray Lee was taken into care at an old people's hospital because he was of "such diminished capacity", the documents said.
The pair are pushing to be paid the business's profits since 2000 as well as the difference between the $200,000 paid and the company's true value.
A lengthy legal battle culminated at the High Court in 2012, where Greg Lee tried to strike out the proceedings because they were "frivolous or vexatious".
He denies his siblings' claims, with support from HDP accountant Adrian Williamson who said Greg Lee's purchase of the company was effectively him "receiving his inheritance early".
"My firm has retained key documents in respect of the advice we gave to the Lee's throughout 1995-1997 regarding a means of transferring ownership of the company to Gregory Lee that was fair between as him and his siblings.
"Gregory was in effect receiving his inheritance early by paying the agreed sum of $200,000."
Today's Court of Appeal judgment delivered by Justice Clifford stated Ray and Joyce Lee understood their inheritance - a $195,000 Rotorua home, a $275,000 factory and the $333,000 business - would be divided evenly between their four children.
If Greg Lee was also to inherit the shares in the business, he would be required to pay his siblings the excess $133,000, Justice Clifford said.
Justice Clifford said, while the underlying facts were not clear, the court had found the claims brought by Robert Lee and Helen Heard were equitable.
"The essence of the claim...is based on the family context, that is the relationship between elderly and weakening parents and the son who was (it is alleged) by himself running the family business in the last years of his parents' lives," he said.
Robert Lee and Helen Heard's appeal was allowed, and the previous High Court decision in favour of Greg Lee was quashed.
The decision means the High Court proceedings "remain on foot" but the family feud would also be suitable for an alternative dispute resolution process, Justice Clifford said.
