Pre-heat oven to 350°F. Use butter to grease a 1lb loaf pan (8.5" X 4.5") and line with parchment paper (butter will allow parchment paper to stick to the pan).
In a large bowl mix all-purpose flour, baking powder, and salt. Mix until combined.
In a separate bowl, add room temperature butter and sugar. Beat with a mixer at medium speed for 4-5 minutes until the mixture is light and fluffy.
Slowly add eggs into the butter mixture a little at a time. Make sure the eggs are fully incorporated before adding more (do not rush this process). Add in sour cream.
Sift dry ingredients (all-purpose flour, baking powder, and salt) into the butter mixture. Fold in dry ingredients with a rubber spatula until combined. Be sure not to overmix. Add vanilla extract, lemon juice, and lemon zest. Fold into batter.
In a separate bowl, add matcha and milk. Whisk until matcha is smooth and no lumps are visible. Add a quarter of the batter in with matcha and fold together with a rubber spatula until combined.
Use a rubber spatula to add dollops of matcha batter into the other batter. Carefully fold the matcha into the batter a few times until you start to see a swirl pattern (no not overmix or the batter will end up turning solid green). Pour batter into the loaf pan and smooth out the top without mixing any further.
Bake for 55 minutes. A skewer should come out clean when inserted into the cake. That is the indicator that the cake is done. A skewer inserted into the middle should come out clean. Let the cake cool in the loaf pan for around 15 minutes. Before removing it from the pan.