Natural fiber yarn comes in an astounding variety!
With all yarns, it is best to get a little more than the amount you think you need for your project to be assured of the same exact color(s), i.e., yarn from the same dye lot.
With hand dyed yarns, each shank may be slightly different, so take this into account.
Natural yarns can be made from any number of products including: sugar cane fiber, animal fur, merino wool, alpaca, mohair, beech wood fiber, silk, cotton, and more.
Many times they are a blend of natural fibers or contain a percentage of synthetic fiber, such as nylon.
An excellent source of less expensive yarn is KnitPicks
Another option is to go to the Brown Sheep Co.'s natural fiber website. They apparently do not sell directly anymore but you can search your location to find a retailer near you.
Cestari Sheep & Wool Company in Virginia is a small family-owned and operated American manufacturer of knitting and crocheting yarn. All wools and cottons are grown and processed in the U.S. and the lanolin is not removed from the wool. Expect to pay around $10 a skein.
Elsebeth Lavold yarn blends may include hemp or silk.
For a higher end option, consider 100% hand dyed merino wool yarns. These consist of color coordinated mini skeins. Good for two pairs of dog socks or perhaps one or two dog sweaters.