Even though this post is three-years old at this point, I'm just going to clear this up for anyone in the future who comes across this page.
In HYPOthyroidism, the mechanism for amenorrhea is decreased free T3/T4 causing upregulation of TRH, thereby increasing prolactin secretion, which decreases LH/FSH secretion.
In HYPERthyroidism, amenorrhea occurs because free T3/T4 increases sex-hormone binding globulin (SHBG) secretion from the liver, thereby decreasing the ratio of free-/bound-estradiol (and in a male, testosterone and DHT). Since higher free-estradiol concentrations are ultimately responsible for the ovulation-inducing LH-spike, decreased free-estradiol would decrease the probability of the LH-spike occurring.