1. Pure raspberries in a blender until smooth. Strain through a fine-mesh sieve into a medium bowl.
2. Whisk eggs, granulated sugar, and lemon juice in another medium bowl.
3. Whisk in pomegranate juice, salt, and 1/4 cup raspberry pure until smooth, then whisk in flour until combined. (Reserve remaining raspberry pure for other use.)
4. Pour filling into crust and bake until filling is set and slightly golden at the edges, about 20 minutes more.
5. Transfer pan to a wire rack and let cool completely. Loosen edges with an offset spatula or butter knife, then use parchment paper overhang to remove bar from pan.
6. Place bar on parchment on a cutting board and cut into 4 pieces lengthwise, then 4 pieces crosswise to make 16 bars. Dust bars with powdered sugar.
7. Do Ahead
8. Raspberry pure can be made and chilled in an airtight container for up to 3 days. Assembled bars can be chilled in a single layer in an airtight container for up to 5 days.
9. Cooks' Note
10. Remaining raspberry pure can be folded into yogurt or poured over ice cream.
11. Position rack in center of oven and preheat to 350F. Grease 8x8" baking pan with butter or nonstick cooking spray. Line pan with parchment, leaving a generous overhang on all sides, and grease parchment with butter or nonstick cooking spray.
12. Pure flour, powdered sugar, salt, and lemon zest in a food processor until combined.
13. Add 6 Tbsp. butter and pulse just until dough forms.
14. Press dough into bottom of prepared pan and about 1/2" up sides. Chill at least 30 minutes.
15. Prick bottom of crust with a fork and bake until light golden brown, about 20 minutes.