In a bowl, whisk flour, baking powder and salt. Use electric mixer at medium-high speed to beat butter and 1 cup sugar until light and fluffy, about 2 minutes. Scrape down sides of bowl with a rubber spatula. Add egg, lemon juice, zest and vanilla, and mix well. On lowest speed, slowly add flour mixture, beating just until a soft dough forms. Divide dough into 2 flat disks. Wrap each disk in plastic wrap; chill at least 3 hours.
Place racks in upper and lower thirds of oven and preheat to 400ºF. Line 2 baking sheets with parchment. Remove one disk from refrigerator and allow to soften slightly. On a floured surface, roll out dough to 1/4-inch thickness. Using a 3-inch cookie cutter, cut out as many cookies as possible. Gather and reroll dough scraps; cut more cookies. Transfer cookies to baking sheets, spacing them 1 inch apart. Sprinkle with sugar. Bake until edges are lightly brown, 8 to 11 minutes, switching baking sheets from top to bottom and front to back halfway through. Let cool on sheets on wire racks for 2 minutes, then transfer cookies to racks to cool completely. Repeat with remaining dough.
Line a baking sheet with parchment; place in freezer. Remove sorbet from freezer and allow to soften slightly. Lightly spread a heaping tablespoon of sorbet in center of a cookie, bottom side up. Top with another cookie, bottom side down; gently press together. Place on baking sheet in freezer. Repeat until all sandwiches have been filled. Freeze sandwiches until sorbet is firm, about 30 minutes. (For longer storage, wrap sandwiches in plastic wrap after they are firm.)