Preheat your oven to 350°F (175°C). Grease a loaf pan.
Mix sugar, eggs, sour cream, lemon zest, lemon juice, vanilla, and oil until smooth.
Sift flour, baking powder, and salt together.
Gradually mix dry ingredients into wet until just combined. Set this batter aside.
Beat cream cheese and powdered sugar until smooth.
Pour half the batter into the pan. Add half the cream cheese mixture in dollops. Swirl with a knife. Repeat with the remaining batter and cream cheese mixture.
Bake for 65-70 minutes. If the top browns too quickly, cover with foil for the last 20-30 minutes.
Let the loaf cool in the pan, then remove and slice once completely cool.