Place a metal mixing bowl and beaters in the freezer for 10 minutes to chill for the whipped cream.
Preheat the oven to 355°F. Lightly grease a 24-cup mini muffin tin.
Whisk the instant lemon pudding mix with the cold milk and lemon juice for 1 minute. Cover and refrigerate to thicken while you bake.
Stir graham cracker crumbs with melted butter until every crumb looks moistened. Divide about 2 heaping teaspoons into each muffin cup and press firmly into a flat base. Par-bake for 4 minutes, then set the pan on a rack for 2 minutes. Keep the oven on.
For the cookie dough, beat softened butter and granulated sugar on medium-high until pale and fluffy, 2 to 3 minutes. Mix in the egg, vanilla bean paste, and lemon zest until smooth.
In a separate bowl, whisk together flour, dry lemon cake mix, baking powder, and salt. Add to the butter mixture on low speed just until a soft dough forms; do not overmix.
Scoop a rounded tablespoon of dough onto each warm graham base and gently flatten the tops with damp fingertips. Bake 10 to 12 minutes, until edges are set and tops look matte but centers are still soft.
Cool in the pan for 5 minutes. Lightly oil the back of a 1-teaspoon measuring spoon and press into the center of each cookie to create a well. Cool 10 minutes more, then twist each cup to release and transfer to a rack to cool completely.
Make the whipped cream: In the chilled bowl, beat heavy cream with cream of tartar on medium speed until slightly thick and foamy, 1 to 2 minutes. Increase speed, slowly add powdered sugar, and whip to medium-stiff peaks. Reserve 1/2 cup for topping.
Fold the remaining whipped cream into the chilled pudding in two additions until light and mousse-like. Refrigerate 10 to 15 minutes to firm up for piping.
Pipe or spoon lemon mousse into each cooled cookie cup. Finish with a small swirl of the reserved whipped cream and a fresh grate of lemon zest.
Refrigerate the filled cups at least 20 minutes before serving. Store covered and chilled for up to 3 days.