A common problem for students of English is when to use ‘a’ or ‘an’ and when to use ‘the’.
In the example above, ‘the’ should replace ‘a’. This is because there are many kinds of diet: low-fat, high-protein, pureed, etc. If the recommendation is for one particular diet, we write ‘a low-fat diet’.
The use of articles can be confusing, even for native English speakers.
We write ‘the’ when there is only one of something e.g. the Emergency Department or when the writer and the reader are clear which one is being discussed e.g. the local council will provide a home-care nurse.