If you can't find Meyer Lemons, use regular lemons.
Preheat the oven to 350 degrees fahrenheit.
Grease an 8 1/2 x 4 1/4 x 2 1/2-inch loaf pan. Line the bottom with parchment paper and butter and flour the entire pan.
Sift the flour, baking powder, and salt together into a medium bowl.
In a large bowl, whisk together sour cream, 1 cup of the sugar, eggs, lemon zest and vanilla. Slowly add the dry ingredients into the wet, whisking to combine (I did this in 2-3 additions). Use a rubber spatula to fold the vegetable oil into the batter until it’s fully incorporated. Pour into the prepared pan and bake for about 50 minutes, or until a cake tester stuck in the center of the loaf comes out clean.
Combine the 1/3 cup lemon juice and remaining 1/3 cup sugar in a small saucepan over medium heat and cook until the sugar dissolves and the mixture is clear. Set aside.
When the cake is done, allow it to cool in the pan for 10 minutes before removing it and placing it on a baking rack over a sheet pan. Use a cake tester, wooden skewer, or toothpick to carefully pierce holes throughout the cake (I used a toothpick so the holes wouldn’t be too obvious, but a skewer might have made deeper holes in the cake, allowing more syrup to get through).
While the cake is still warm, pour the lemon-sugar mixture over the cake and allow it to soak in.
Do this part right before you plan to drizzle the glaze over the cake.
In a small bowl, combine the confectioners’ sugar and lemon juice, whisking to form a smooth glaze. Pour over the cake. Slice and serve with fresh berries, whipped cream, or ice cream.
This is Ina Garten's Recipe