One of the questions that comes up on the Peak Testosterone Forum from time to time is whether or not LH (luteinizing hormone) levels and receptors are important in men, especially in those on TRT (testosterone replacement therapy). The reason this questions gets asked is that most men know that LH's primary male function is to stimulate the testes to produce testosterone. So, if a man is on testosterone therapy, then he doesn't need LH any more, right?
Unfortunately, the answer is not so simple and below I will show you Three Different Tissues in Men Where LH Likely Plays an Important Role. There is a lot more to this subject - for example, how it potentially argues for low dose HCG as a complementary therapy in TRT - and so I hope you will visit my pages The Benefits of HCG with TRT and My List of HCG Pages.
NOTE: HCG is not LH. Yes, it is a similar hormone and binds onto the luteinizing hormone receptor. However, there are key differences.
1. Brain, Cognitive and Hippocampal Tissue. There is some preliminary evidence that LH and the LHCGR play important roles in many key parts of the brain:
"Specific receptors for LH/hCG have been identified in the hippocampus, dentate gyrus, hypothalamus, cortex, brain stem, area postrema, cerebellum, choroid plexus, ependymal cells, glial cells, neural retina, pituitary gland, and neuron processes of the spinal cord." 
The role of LH may be particularly important in the hippocampus, the center of memory and ground zero for almost everything that you do consciously as a human. In fact, the hippocampus has the highest density of these receptors. Does anyone really believe that these receptors are vestigal, i.e. no longer serve any purpose?
In my opinion, it stands to reason that having an almost undetectable LH level, which is what happens with a man on a solid TRT protocol, may not be a good idea. Interestingly enough, what has been confirmed in men, women and animals is that high luteinizing hormone is hard on memory. 
2. Adrenal (Cortisol Production). It turns out that the luteinizing hormone receptor (LHCGR) can actually play a role in Cushing's Disease upon rare occasion. Check out why below:
"Transient pregnancy-induced Cushing's syndrome (CS) is extremely rare, with only several cases reported in the literature. Ectopic LH/hCG-receptors (LHCGR) in the adrenal gland have been suggested to be involved in the pathogenesis of this condition. We report the clinical, molecular, and genetic features of a patient with pregnancy-induced CS. A 29-year-old female patient developed CS during multiple pregnancies, leading to repeated miscarriage. Signs and symptoms of hypercortisolism resolved soon after delivery or abortion, only to recur in subsequent pregnancies. In the non-pregnant state, hCG stimulation testing resulted in elevated cortisol levels." 
So clearly HCG and LH can increase cortisol through activity on the adrenal gland. So, is the ultralow LH from TRT a possible risk factor for low cortisol in the longer term? Is this one of the reasons that some men on TRT sometimes report low cortisol. I can tell you that I just pulled my morning cortisol and it was low, but clearly more studywork is needed. But it is definitely in the realm of possibility that very low LH like I have could somewhat negatively impact the adrenals.
3. Vascular Effects (Angiogenesis via VEGF and EGF). As I mentioned in my page on Some Potential Concerns of Too Much HCG, HCG is a powerful stimulant of angiogenesis. Now angiogenesis is a necessary part of life in order to revascularize tissues but can contribute to cancer if too high. Here is just one of many examples in the medical journals: "in conclusion, high levels of LH promote angiogenesis in ovarian cancer via the PI3K/AKT-mTOR pathway."  So could super low LH lead to the other extreme?
NOTE: Tying into this is the research showing that LH/HCG may play a role in developing Down's Syndrome, which is caused by an extra chromosome.
1) Endocr Pathol, 2009 Winter, 20(4):256-61, "Case report: Adrenal LH/hCG receptor overexpression and gene amplification causing pregnancy-induced Cushing's syndrome.
2) Oncol Rep, 2012 Jun, 27(6):1873-8, "Luteinizing hormone facilitates angiogenesis in ovarian epithelial tumor cells and metformin inhibits the effect through the mTOR signaling pathway"
3) Semin Reprod Med, 2001, 19(1):103-9, "Neural actions of luteinizing hormone and human chorionic gonadotropin"
4) Horm Behav. 2010 Nov;58(5):705-13, "Low luteinizing hormone enhances spatial memory and has protective effects on memory loss in rats"
5) J Alzheimers Dis, 2010;19(3):943-51, "Higher luteinizing hormone is associated with poor memory recall: the health in men study"
6) Hormones and Behavior (Impact Factor: 4.63), 61(4):479-86, "The role of testicular hormones and luteinizing hormone in spatial memory in adult male rats"