In a mortar, grind lavender flowers with the pestle.
In a medium bowl, cream together ground lavender flowers, butter, sugar, vanilla extract, and lemon extract. Add flour and salt; mix until combined (dough should be soft but not sticky). Refrigerate 1 to 2 hours or until dough is firm.
Prepare Lavender Frosting; set aside.
Preheat oven to 325 degrees F. Remove dough from refrigerator.
On a lightly-floured surface, roll dough approximately 1/4-inch thick with your rolling pin. Cut into desired shapes with your favorite cookie cutters and place onto ungreased cookie sheets.
Bake 12 to 15 minutes or until cookies are lightly browned around the edges. Remove from oven and cool on wire cooling racks. When cool, frost with Lavender Frosting.
In a small plastic bag, combine powdered sugar and dried lavender flowers. Let stand at least 1 day before using. When ready to use, sift the mixture into a medium-size bowl; discarding lavender flowers.
Add milk and corn syrup, mixing well. Additional powdered sugar or milk may need to be added (enough milk to make frosting easy to spread). Spread on baked, cooled cookies.
NOTE: Courtney and Brittany added some lavender food coloring to the frosting mix. This is something that I do not usually do.
Lavender Tea Cookies Recipe: https://whatscookingamerica.net/Cookie/LavenderCookie.htm