Combine the 2 teaspoons of lime juice with the coconut milk, let stand for 5 minutes.
In a large bowl, cream together the coconut butter and ¾ cup sugar until light and fluffy. Beat in the egg, then stir in the lime zest and milk mixture.
Combine the flour, baking powder and baking soda in a medium bowl. Blend into the creamed mixture. Drop by rounded spoonfuls onto the ungreased cookie sheets.
Bake for 8 to 10 minutes, until the edges are light brown. Allow cookies to cool on baking sheets for 5 minutes before transferring to a wire rack to cool completely.
To make the glaze, whisk together the remaining 2 tablespoons lime juice and sugar until the sugar dissolves. Brush onto cooled cookies.
Recipe by Go Dairy Free at https://www.godairyfree.org/recipes/coconut-lime-tea-cookies