Does growth hormone deficiency lower testosterone levels?

No: Your pituitary controls a number of hormones including thyroid, growth, testosterone & estradiol, among others. While growth hormone deficiency won't "lower" testosterone, pituitary damage leading to growth hormone deficiency can also lead to hypogonadism or low testosterone. It's also common to have a defect in just one hormone rather than all. Traumatic brain injury is not a major concern.