I have seen a woman who had lumpectomy and radiation to the left breast
for breast cancer.  She produced very little milk on the left side, but
luckily enough on the right to be able to breastfeed exclusively for a
long time.

I think that if the breasts got a fair amount of radiation, it is
unlikely she will produce an adequate milk supply.  However, I agree
that you should encourage her anyways, not looking at the amount she
produces and just enjoying breastfeeding even with a lactation aid.

Jack Newman, MD, FRCPC