There are low fat diets that are too severe or ignore body needs.

Dieting should be with the direction of your physician.
Physician-approved diets, such as those developed by the Mayo Clinic, are not entirely fat-free, but maintain a balance.

Also helpful is this very good list from the UK, Basingstoke and North Hampshire. (Attention paid to gallstones)

http://hampshirehospitals.nhs.uk/media/168017/low_fat_diet_gallstones_.pdf