The filepaths C:\HaxeToolKit\haxe and C:\HaxeToolKit\neko both exist. I unistalled, then reinstalled haxe, then added all the filepaths to user-variables instead of system variables (as I do not have required permissions to change system variables). This worked and I was able to do haxelib run lime setup. Does this mean that lime is installed and I don't have to run lime setup windows?
EDIT: So I realized that I had added the filepath C:\Users\user\HaxeToolkit\haxe allowed me to use the haxelib command. If I follow the same format for flixel, lime, and openfl, my question now becomes, where are the commands installed to (starting from the library folder)?