Ok here goes to the best of my abilities:
If your testicles are shut down by exogenous drug use, LH production should be lessened as a result (or perhaps more accurately the cause).
Winstrol is a progesterone-receptor modulator, this entails that prolactin will more likely than not be unaffected.
TSH refers to Thyroid Stimulating Hormone. This one is tricky.
Certain things will suppress the amount of TSH produced. These include dopamine agonists (which you probably are not on), glucocorticoids (hormones that deal with glucose metabalism, notably cortisol is you are stressed out), and yes AAS use as well.
But whether or not it will register or the degree to which it registers depends on how it is tested for. TSH controls the release of thyroxine (T4) and small bits of triiodothyronine (T3). The majority of the this stuff is bound in thyroid binding globulin (TBG) much like androgens are bound up in SHBG. The use of AAS decreases the amount of TBG and therefor the total amount of T3/T4, whilst the free or circulating T3/T4 remains more or less unchanged.
What does this mean? Very little I just wanted the mind-exercise of explaining it. The reason TSH is tested for is that high levels of it is indicative of low T4, and thus hypothyroidism, which is bad news for the hormones it secretes and can lead to a host of problems, which is why its tested for. I dont know how it is tested for, directly or indirectly. Either way its very unlikely anything will register here out of the ordinary.
Prolactin levels are tested for because it can have alot of the effects of high estrogen (gyno for example) while also causing erectile disfunction.
LH hormone is tested as it governs your nuts pretty much. You may have low levels of LH hormone and maybe be given some hcg (a LH analogue) or you may have high LH combined with low testosterone indicating an insensitivity to the LH itself.
The doctor looks at all these things to see not only if your testosterone is low, but why as well. From what I understand not much will register out of the ordinary. You may have a lower T than normal and thus a lower LH than normal but to what degree I cannot say.