In a bowl, using your fingers rub the thyme in the sugar relaxing the oils from he thyme to fragrance the sugar. This process with infuse the sugar with the thyme scent and a little flavor.
In an electric mixer, beat butter and sugar until combined.
Add in the vanilla and lemon extract.
Add in the flour and salt and blend on low until incorporated.
Refrigerate the dough for about 30 minutes so it's cold, but not too hard to roll out.
Add the dough on a flour surface and roll out about 1/2-1" thick. Use a cookie cutter, round or flower shape to cut the shapes.
Line a cookie sheet with parchment paper to bake the cookies on.
Bake in a preheated 350 degree oven for about 15 minutes until cookies are just about to turn golden brown. I like to take them out before they turn gold.