Preheat oven to 350 degrees F. Adjust rack in oven to middle.
Grease or spray the inside of a 10" tube pan. Whisk dry ingredients together; flour, baking powder, baking soda and salt.
In a stand mixer fitted with paddle attachment, beat butter and 1 cup plus 2 Tablespoons sugar, and lemon zest together until light and fluffy, scrapping down sides of bowl as necessary, about 3 minutes.
Add eggs, one at a time, beating well after each addition, about 20 seconds. Scrape down sides of bowl. Add 4 teaspoons vanilla, mixing to combine.
Reduce speed of mixer to low, add 1/3 flour mixture and 1/2 sour cream, mixing to blend, just until combined about 5 to 10 seconds. Repeat with 1/3 flour mixture and remaining sour cream, mixing just until combined. Add remaining 1/3 flour and mix for 10 seconds. Use a rubber spatula and make sure all of the flour is combined.
Reserve 1/4 cup batter and pour 1/2 cup batter into the tube pan. Reserve remaining 1/2 cup, in addition to the 1/4 cup batter.
No need to rinse out mixing bowl. Beat cream cheese, 5 Tablespoons sugar, lemon juice, and remaining 1 teaspoon vanilla on medium speed until light and smooth. Fold in 1/4 cup batter. Mixing until smooth.
Drop cream cheese mixture into tube pan, avoiding edges of pan and smooth with an offset spatula.
Spread remaining 1/2 cup batter and spread over cream cheese filling. Using an offset spatula to swirl the filling into the cake, avoiding edges and sides of pan. Rap or drop cake pan 2 or 3 times to dislodge any bubbles.
Bake at 350 degrees for 45-50 minutes or until a long stick inserted in the cake part (not the cream cheese part) comes out clean.
Cool cake in pan on wire rack for an hour. Remove cake from pan and cool top up another hour or until completely cool.
Wrap any remaining cake in plastic or an airtight container.