Preheat the air fryer to 320°F. Grease a 7-inch bundt pan thoroughly with baking spray, getting into every ridge, then dust lightly with flour.
Whisk the cake mix and dry pudding mix together in a large bowl.
Add the eggs, sour cream, water, oil, lemon juice, zest, lemon extract, and vanilla. Beat on medium 2 minutes, scraping the bowl once.
Pour batter into the prepared pan, filling three-quarters full. Do not overfill.
Tent foil loosely over the pan. Air fry 20 minutes at 320°F.
Remove the foil and air fry another 12–18 minutes, until a toothpick inserted in the thickest part of the ring comes out clean (200–205°F internal).
Cool in the pan 10 minutes. Run a knife around the edges and the center tube, then invert onto a wire rack. Cool completely.
Whisk powdered sugar with lemon juice, one tablespoon at a time, until it ribbons off the whisk. Pour over the cooled cake and finish with zest.