Preheat your oven to 350°F and line baking sheets with parchment paper.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3 minutes.
Beat in the eggs one at a time, then add the lime juice, lime zest, and vanilla extract.
In a separate bowl, whisk together the flour, graham cracker crumbs, baking soda, and salt.
Gradually mix the dry ingredients into the wet ingredients until just combined.
Drop rounded tablespoons of dough onto prepared baking sheets, spacing them 2 inches apart.
Bake for 10-12 minutes until edges are lightly golden. Let cool on the baking sheet for 5 minutes before transferring to a wire rack.
For the glaze, whisk together powdered sugar and lime juice until smooth. Drizzle over cooled cookies and let set for 15 minutes before serving.
