food restriction

I want to Lucy cannot eat dairy products due to some kinds of reason under's advice. Shall I say :

Lucy is under food restriction of dairy products upon doctor's advice.

I don't want to say she cannot eat dairy product only as I want say it more professional

Thank you.

Lucy cannot eat dairy products as her doctor has diagnosed her as lactose intolerant.

I would suggest not trying to sound professional. Keep it simple and you'll find it easier to express yourself. Your listener will also find you easier to understand!

Another option:

'Lucy's doctor has advised her not to eat dairy products.'