I have avascular necrosis in my right hip, can it cause lower right back pain?

Indirectly : Referred pain from hips typically occur in groin or down thigh. That beig said any referral pattern is possible. A possibility may also be your hip avn has led to a dysfunction walking/gait pattern leading to abnormal stresses on back/sacroiliac regions which may cause pain. Get formal eval by a specialist who manages back pain.

Yes: Problems with hip pain may eventually cause issues with your back due to how the body tries to adjust to pain by favoring the non painful joint leading to misalignment of your back.