Could a lesion within the right medial ilium bone cause pain in my hip just below my back and into the right side of my bottom?

Yes, possibly: Your ilium is the large wing-shaped pelvic bone. The medial portion of your ilium is the part closer to your spine. A lesion in your ilium could cause pain in your back and buttock area, but so could many other things including a compressed nerve (from a bulging disc), a tight piriformis muscle, or inflammation in your sacroiliac joint. It sounds like your pain "refers", making me think nerve.