After a lumpectomy for stage 1 breast cancer, will a doctor always assign that you get radiation treatment, or does it depend on the patient?

Usually yes. Most of the time rdiation treatment is needed to provide comparable longterm survival benefit in comparison to mastectomy. In women over 70 years old and if the cancer is esterogen receptor positive, endocrine therapy may be substitued with satisfactory results. You need to talk with your surgeon, medical oncologist as well a radiation oncologist to see what your particular cirmumstance will be.
Most likely. Trials have shown that lumpectomy folllowed by radiation for early stage breast cancer is equivalent to mastectomy. All women benefit from an improvement in local control, that is preventing the cancer from coming back in the breast. Women younger than 70-75 also are likely to live long enough to see a survival advantage after radiation therapy as well.