I don't understand why doctor's let Mum's think that if their baby has lactose intolerance they must give up breastfeeding!

Breastmilk is NOT dairy. Cow's breastmilk is (dairy).

If your child is lactose intolerant and you wish to breastfeed, then by all means DO!  BUT!!! You, MUM, need to give up dairy. All of it. Dairy proteins transfer into your milk and thus cause tummy troubles for baby.

Eating dairy free for six months or more is not a big deal and barely a sacrifice considering what the benefit to baby will be.

I'm including these links for more detailed and specific information by medical professionals.
Dairy and other food sensitivities in Breastfed Babies (kellymom.com)
Is My Baby Lactose Intolerant?

And finally, if you are breastfeeding your baby and your doctor suspects your baby to be allergic to milk or lactose intollerant and tell you to stop breastfeeding...

Tell him/her YOU ARE NOT A COW!!!!