Cream together butter, shortening, sugar, and brown sugar until creamy. Beat in egg, lime juice, lime zest, and vanilla until fluffy.
Stir baking soda, salt, and flour into mixture adding flour a little at a time. Stir in white chocolate chips and chopped pecans.
Use a 1" cookie scoop to scoop balls of dough onto parchment lined baking sheet. Place 2" apart. Bake cookies for about 15 minutes, until they are slightly browned. Remove from oven and let cool a minute on baking sheet, then transfer them to a cooling rack.