How long after a lumpectomy would radiation therapy begin depends on whether chemotherapy has been recommended or not. That is because generally speaking in the sequence of treatments, chemotherapy comes before radiation. But regardless of whether it is chemotherapy or radiation, the factor determining the beginning of next treatment is how well the incision of lumpectomy has healed and whether the infection site has become infected or not. Both chemotherapy and radiation therapy can delay the healing process and chemotherapy in particular can weaken the immune system and cause any infectious process to spread in the body.
If no chemotherapy has been recommended, as a rule of thumb we would like to leave at least four weeks between surgical procedure and the beginning of radiation therapy but it is all right to delay it up to eight weeks for invasive cancer and up to twelve weeks for DCIS. But once the interval is increased more than that, one would be concerned that the efficacy of radiation would begin to decrease.
Please bear in mind that the above is in regards to external beam radiation therapy because in APBI or Accelerated Partial Breast Irradiation using a variety of catheters such as The SAVI Applicator, MammoSite or Contura Balloon radiation can begin within a couple of days after insertion of these applicators and as soon as the pathology report is finalized.