Having an increase in free testosterone from a supplement likely would decrease LH, but remember the role of LH is to produce testosterone.
So if your free testosterone is going up, your body does not need to produce as much T, so LH will go down a little. The best way to combat this, or instead make the whole free testosterone increase even more effective would be to use something that increases free T like Divanex in combination with something that increases LH, like PowerFULL or L-Dopa(mucuna pruriens)