Preheat your oven to 350°F (175°C).
Grease and flour a 9x5 inch loaf pan.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt.
In a large bowl, beat softened butter and sugar until light and fluffy.
Add eggs one at a time, mixing well after each addition.
Mix in the Meyer lemon juice, zest, and vanilla extract until combined.
Gradually add the flour mixture to the wet ingredients, mixing until just combined.
Pour the batter into the prepared loaf pan and smooth the top.
Bake in the preheated oven for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes before transferring to a wire rack to cool completely.