How can a person have had cancer and survived 30 years without chemotherapy and radiotherapy?

It would have to depend upon where the cancer was located, what type of cancer it was, and how far advanced it was, if the patient lived for years without chemo and radiation. Chemo and radiation are NOT always necessary.
My aunt developed breast cancer when she was in her late 30's, back in the late 1940's. She had her breast removed and she never had any chemo or radiation treatments after the surgery. She lived a perfectly healthy life afterward, and died when she was in her late 90's of "old age".

i am a 51 year old man who has Hepatitis C which led too cirrhosis of my liver which eventually too me developing stage one liver and kidney cancer and i found that out by having a biopsy done on both of them and thankfully i have had none of that stuff or any type of medication yet

Some types of cancer only require surgery.
Sometimes quite minor surgery.
Depending on the type of cancer and tbe stage when removed this might be totally unremarkable.

There are a few possibilities:
1. Her immune system successfully fought the cancer.
2. She was initially misdiagnosed.
3. She's lying.

Here's a wild Idea...maybe she lied. We see it all the time here with people pretending that they have cancer and posting the same thing over and over. Some people just need to have the spotlight all the time no matter what lies they have to tell to get there.

That being said some cancers aren't helped with chemo and only respond to surgery or other methods of control.

She wouldn't be the first..

1. She has a very strong will power.
2. In medical books, here is a fact recorded. One sage, by name Ramana Maharshi from India had stomach cancer and when malignant cells were increasing, his stomach was bulging. Just with a small hit by his hand on his stomach, the bulged stomach was becoming normal for years together.
3. Deep and total committed faith in the GOD cures many a no. of incurable ailments.

Probably wasn't cancer in the first place.

It's impossible to say without knowing what kind of cancer she has and what treatment she has done. Maybe it's a simple basal cell carcinoma. Maybe she had surgery to remove a tumor. Maybe she has an incredibly rare smoldering cancer- meaning that it's there, but it doesn't do much for a long time (there's a kind of lymphoma that's like this.)

Maybe she's exaggerating- maybe she was diagnosed with a "pre-cancerous" condition. Maybe she's lying.

Whatever it is, her "it's all in the mind" is bull. Ask her how she explains children who die of cancer.

As someone who works in pediatric oncology and also recently lost a teenage family member to cancer, I find that "it's all in the mind" to be so offensive. When a 2 year old dies of cancer, it's not because they gave up or didn't fight hard enough. It's not because of negative thinking or fear. It's because the cancer was too powerful and treatment did not work. That's it.

Our hospital lost an infant to cancer last year. Please explain how that is due to his mindset.

Some types of cancer grow very slowly, you didn't mention whether the woman had any surgery, and it's possible the initial diagnosis was mistaken.