Preheat oven to 350 degrees. Grease bottom of 2 quart rectangular baking dish; set aside.
For crust: In medium bowl, combine crushed pretzels, melted butter, and 2 tablespoons sugar. Press mixture into bottom of prepared baking dish. Bake for 10 minutes.
Meanwhile, for filling: In large bowl, combine cream cheese, 2/3 cup sugar, and vanilla. Beat with electric mixer on medium to high speed until combined. Add eggs; beat on low speed just until combined. Stir in lime peel and lime juice. Pour filling over crust. Sprinkle with nuts.
Bake for 20 to 25 minutes or until center is set. Cool in baking dish on wire rack for 30 minutes. Cover and chill for 4 to 24 hours (top will crack slightly). Cut into bars.