Beat cream cheese, sugar, milk, lemon zest and juice in medium bowl with mixer until blended. Gently stir in marshmallow creme.
Reserve about 3 Tbsp. cookie crumbs. Spoon 1 Tbsp. of the remaining cookie crumbs into each of 10 parfait glasses; top with 2 Tbsp. cream cheese mixture. Cover with layers of strawberries, remaining cookie crumbs, remaining cream cheese mixture and blueberries.