This is almost certainly Alfred Bester's The Computer ConnectionThe Computer Connection (aka Extro) which has many points of similarity with your list: group of immortals, Native American bride, power struggle, etc). Flipping through the book, I found the cancer reference too, although it's some kind of awful leprosy/cancer combination called Lepcer. It can strike the immortals if they get wounded too badly.
Here's the fast marriage quote:
I looked at the Chief, completely bewildered.
"You've just married my sister," he said casually.
I went into shock.
The lion thing is one of the immortals who got Lepcer.
After a moment I saw that the lion was standing on its hind legs. After another I saw it was a man wearing a lion mask. And then I realized it wasn't a mask. It was a deformed face.
"Oh God! The big L!"