BEAT cream cheese, 1 Tbsp. milk and the sugar in medium bowl with wire whisk until well blended. Stir in lemon zest and juice. Gently stir in 1-1/2 cups of the whipped topping. Spread evenly onto bottom of crust. Reserve several strawberry halves for garnish. Arrange remaining strawberry halves on cream cheese layer; press gently into cream cheese mixture.
POUR 2 cups milk into large bowl. Add dry pudding mixes. Beat with wire whisk 2 min. Let stand 5 min. or until thickened. Gently stir in 1 cup of the remaining whipped topping. Spoon over strawberries in crust.
REFRIGERATE 4 hours or until set. Top with the remaining 1/2 cup whipped topping and the reserved strawberry halves just before serving. Store leftover pie in refrigerator.