I have a few clients who tried grain free low carb (both for health & philosophical reasons) and I have to say its a bad idea.
By avoiding grains they always suffer from digestive problems such as constipation, etc.
It limits you to fruits, veggies (which you have to eat a load of to get enough fibre to avoid constipation) and only a few starchy carbs such as sweet potatoes & carrots.
I think grain free & low carb are fine by themselves, but combining the two is a terrible idea unless you want to feel uncomfortable & not fully replenish muscle glycogen (very important to training).