The list of dietary fiber sources is fairly long. It is usually possible to get a certain amount of fiber from permitted foods, especially vegetables, nuts, and seeds. If you aren't sensitive to grains, you can add certain brans to your diet. Wheat bran is the least expensive source of insoluble fiber, as long as you remember that at least a third of its carbs are bioavailable. OTOH, oat bran, is not all that good for lowcarbers because it packs so large dose of bioavailable carbs.
Soluble fiber is a bit more difficult to get in quantity from foods.
Good sources include flax seed, seaweed, and avocadoes. Actually, most seeds contain at least some soluble fiber. Look for those that are mostly fiber, since whole grains, too, are seeds with fiber, but their starch far exceeds their fiber content. Don't kick yourself if you can't meet your goals from diet. The bottom line is that most lowcarbers will need to supplement to get the recommended daily amount of fiber.