Heat oven to 350°F. Line a 9x13-inch pan with parchment, leaving overhang.
Press the cinnamon roll dough into an even crust, pinching seams to seal.
Par-bake the crust for 8 minutes. Meanwhile, mix melted butter, brown sugar, and cinnamon.
Beat cream cheese, granulated sugar, and salt until perfectly smooth.
Blend in sour cream, vanilla, lemon juice, then flour; scrape the bowl well.
Mix in the eggs just until combined; avoid overbeating to prevent cracks.
Pour batter over the warm crust and tap the pan to release air bubbles.
Spoon the cinnamon mixture in ribbons over the top and gently swirl with a knife.
Bake 30 minutes, until edges are set and the center still jiggles slightly.
Cool on a rack for 1 hour, then chill at least 2 hours until fully set.
Whisk powdered sugar with milk until smooth; drizzle over chilled bars. Slice and serve.