Preheat oven to 400 degrees F.
In a large bowl, sift together the flour, sugar, baking powder, baking soda, and salt. Add the rosemary and lemon zest, and mix until combined. Quickly blend in the shortening until the mixture resembles coarse meal. Make a well in the center and stir in the buttermilk and strawberries until just blended. Do not over mix.
Turn the dough out onto a well-floured board and knead gently 2 to 3 times. Pat the dough into a circle about 1/2-inch thick. Using a 3 inch round cookie cutter, cut out biscuits and place on a baking sheet.
Bake until golden, about 20 minutes. Transfer biscuits to a rack to cool.
In a bowl, combine the melted butter, sugar, and lemon juice and zest. Brush glaze over warm biscuits.