Is radiation really necessary for an 86-year-old after a lumpectomy of a very small (bb sized) tumor?

This is a really tough question. To me it's a family decision if the person involved can't make the decision.
Many people this age are very frail, and surgery, chemo, or even radiation can be very hard on them. Is this the case?
Skin is generally very fragile at this age - would she heal from the burns?
Since you are unsure, I'd suggest that you get a second medical opinion, at least one from a person who specialized in geriatrics, and that you talk it over with a spiritual counselor is you have someone you trust.
There's no magic answer here. Will the cancer be aggressive or slow- growing. Is she near death anyway? If so, Hospice care to keep her comfortable when the time comes she has pain may be the solution.
Some people want these treatments no matter what their age, and many come through fine. Others don't want the treatments. Some want them and don't do well and regret the decision.
Make sure you've checked all options so you don't have regrets about whatever decision is made. You will know you did your best.
Carol

Treatment of cancer in the eldery should be a joint decison between the elderly person and his/her family, taking into consideration the recommendations of your doctor. Here's an article about the risks and benefits of surgery in seniors.

https://www.agingcare.com/137421