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People that are lactose intolerant shouldn't really drink Soya milk either. You are right to give him rice milk and you can also buy LactoFree milk at the Supermarkets.
Look at the Free From range at your Supermarket - Sainsburys has a good range however the free from range are expensive. You should be able to get them on prescription. Didn't your Doctor mention that?
You will need to look at every food item you buy and see if they contain lactose - including medication.
ds2 and dh are too. We have played it by ear really. Ds2 can eat yoghurt, cheese, butter and foods with a little lactose eg. some biscuits. He can't eat milk, cream and creamy puddings, custard etc or icecream. We find the milk called lactofree is fine with him and tastes much nicer than any alternatives.