Preheat oven to 350° F and grease a 10-inch bundt cake pan. Place greased cake pan in the freezer while you prepare the batter.
Cream the butter until smooth and silky.
In a small bowl, combine lemon zest and sugar. Stir for a few minutes, until lemon releases its natural oils. The sugar will become sticky and fragrant.
Add lemon sugar to butter and beat until thoroughly mixed.
Add eggs, one at a time, beating until incorporated.
Sift dry ingredients (flour, baking soda, baking powder, salt) together in a medium bowl. Combine buttermilk and lemon juice in a separate container.
Add about 1/3 of flour mixture to butter mixture; blend. Add about 1/3 of buttermilk mixture and mix until nearly incorporated. Continue alternating dry ingredients and buttermilk until everything is just blended.
Pour half of the cake batter into the prepared bundt pan and use a small offset spatula or a spoon to even it out. Create a trough in the batter using the back of a spoon. Pour about half of the strawberry swirl filling evenly into trough. Using a butter knife, swirl the jam into the cake batter. Repeat this process with remaining batter and jam.
Bake until toothpick inserted in the center of cake comes out clean, about 45-55 minutes.
Allow cake to cool for about 20 minutes. While still just slightly warm, invert cake onto a cooling rack. Allow to finish cooling completely before glazing.