You don’t need grains to get fiber. A low-carbohydrate diet does not mean it’s inherently a low fiber diet. There are loads of low-glycemic, high-fiber choices. If you insist on a certain level of fiber in your diet, here is a great article to help you build your diet plan.
“Finding foods that are low in carbohydrate yet high in fiber may seem like a challenge. However, almost all non-starchy vegetables and low-sugar fruits are also the highest in both fiber and nutrients.”
https://www.verywellfit.com/high-fiber-low-carb-food-list-2242216