Final answer:
The Gluteus Maximus muscle lower fibers attach to the iliotibial tract, which connects to the lateral aspect of the tibia, and also partially attach to the gluteal tuberosity on the femur.
Step-by-step explanation:
The attachment site for the lower fibers of the Gluteus Maximus muscles is the iliotibial tract which is a thick band of connective tissue that extends from the muscle to the lateral aspect of the tibia. It is formed by the conjunction of the tensor fasciae latae and the gluteus maximus. The iliotibial tract plays a crucial role in the stabilization of the knee and in movements such as walking and running. In addition, it's important to note that the gluteus maximus also attaches to the gluteal tuberosity on the posterior surface of the femur, which is a roughened area extending inferiorly from the base of the greater trochanter. This roughened area is proximally positioned compared to the linea aspera of the femur, which serves as the site for muscle attachments in the thigh.