The twins passed at a hospital in Pennsylvania ... though the exact cause of their death, reportedly last Sunday, has not been disclosed.

Lori & George were born in 1961 ... fused partially at the skull, and sharing 30% of their brains, the parietal and frontal lobes.

Despite predictions the twins wouldn't live past 30, they beat the odds to live more than twice that long.

The pair engaged in their own interests despite their clear physical challenges -- George, who couldn't walk and was pushed around in a wheelchair by Lori, pursued a career as a country singer while Lori won trophies for bowling.

While George's original name was Dori, he actually came out as a transgender man in 2007, changing his name from Reba -- a moniker he took up because he disliked their rhyming names -- to George.

This made them the first same-sex conjoined twins to identify as different genders.

Lori & George lived together in a 2-bedroom Pennsylvania apartment ... alternating nights spent in each room to try to live as independently as possible.

The pair appeared on numerous shows together including "Jerry Springer," "The Maury Povich Show," and "The Howard Stern Radio Show" and they also had documentaries made about them.

Lori and George are survived by their father, six siblings and numerous nieces and nephews.

They were 62.