Preheat oven to 350 degrees F.
In a medium bowl, beat the butter and sugar on medium-high speed with an electric mixer until fluffy, about 3 minutes. Add the lemon zest and juice and mix well. In a separate medium bowl, combine the flour, baking soda, and salt. Gradually add the flour mixture to butter mixture and mix to combine. Shape into a log and wrap in heavy-duty plastic wrap. Refrigerate until firm, at least 2 hours.
Divide the sugar between 2 small resealable plastic bags. Add 8 to 10 drops of 1 color of food coloring to each bag. Shake vigorously to distribute and color the sugar. Put the colored sugar into 2 separate plates.
Slice the log into 1/2-inch thick rounds. Dip the cookies on 1 side into the sugar, making 12 of each color. Arrange the cookies on baking sheets, spacing evenly, and bake until lightly browned, about 12 to 15 minutes. Remove from the oven, allow to cool slightly, then remove the cookies from the pans. Cool completely on wire racks before serving.