This happened with my mil, though it was lung cancer symptom free until it spread to secondary tumours in her brain. Other circumstances incredibly similar to the ones that you describe.
Our children were 11, 9 and 6 at the time. We told them the truth right from the start - she has cancer. Often cancer can be cured, but also it often can't, and hers can't. The doctors think she will live for about a year, but we can't be sure - it could be more but it could be less. No, she won't get better. It's sad, as it's totally normal to cry, to be angry, to think it's not fair, all your feelings are normal. It's important we visit her but if you're upset it's ok to say that you don't want to and just the ones who feel ok go.
They were all sad but they all did brilliantly. Only the eldest coped with the cancer ward at hospital well - she was an absolute hero - the younger two were very cowed by the hospital. However when she came home the 6 year old climbed into her hospital bed and kissed her bald head, and the 9, nearly ten year old pushed her wheelchair into the garden and supported her when she walked a few steps (she lost a lot of weight and he's big for his age, he was probably heavier than her by the end).
She was only in her early 60s and had been very active and healthy til a matter of weeks before diagnosis, the kids were used to foraging in the forest for mushrooms for full days with her, and her being capable and competent and able to look after them. They adjusted astonishingly fast to looking after her, and took her losing her memory, her hearing, her hair, her blader control and her ability to walk in their stride even though it happened over only a few months.
I am very glad we told them the truth and kept visiting. She tried to live to see our youngest start school, it was her goal (abroad, he started at 6.5) but didn't make it. The children were very sad when she died but not shocked, they knew she was dying. If we hadn't told them the truth her death would have been far harder on them, and their visits harder for her and fil - as it was they were ironically what made it easier.
Tell your 7 year old the truth. Mine are sensitive and over empathetic too - that kind of child deserves and needs to be told the truth sensitively and suffers more from white lies than a less thoughtful, more thick skinned child.