Heat oven to 350°F (175°C). Line a 9×9-inch pan with parchment paper, leaving overhang.
Mix cookie crumbs, melted butter, sugar (if using), and salt. Press firmly into the pan.
Bake crust 8–10 minutes, then cool slightly.
Beat cream cheese and sugar until smooth. Mix in vanilla, then add eggs and mix just until combined.
Pour filling over crust and smooth the top. Bake until mostly set with a slight jiggle in the center.
For the lemon topping, whisk lemon juice, zest, sugar, and eggs in a saucepan. Cook over medium-low heat, whisking constantly, until thickened.
Whisk in butter until smooth and glossy. Strain through a fine-mesh strainer into a bowl.
Pour lemon topping over the baked filling and smooth it out.
Bake again briefly until the topping looks set.
Chill until fully firm, then slice into bars. Dust with powdered sugar and garnish as desired.