I had the same invasive lobular diagnosis - stage II. My onco type DX test came back that I was non-responsive for chemo. Radiation only increased long term survival by 2-4%. There is a risk - they say small - of heart issues down the road if they radiate the left side. In my case it was the left side so I chose not to do radiation. There are also the side effects of radiation which is significant burns. ( I know someone who did radiation and she said that her burns where pretty bad) 5.5 years later and my scans are clear. I changed my diet and have a large amount of supplements that I take for cancer prevention.
I hope for you nothing but the best in your treatment - it is your decision to make so do not let the doctors push you in to anything! It is OK to get more than one opinion - see another oncologist for options. The first oncologist we met with said no matter what she was going to do chemo and did not care what the onco test said. The second oncologist who agreed to order it basically said it would be malpractice to give me chemo. You have to be your own advocate!!