Preheat oven to 350 degrees F. Zest 5 Meyer lemons and slice them very thinly. Discard ends from lemons.
Bring a medium pot of water to a simmer and add lemon slices. Lightly simmer lemon slices for 90 seconds. Drain lemon slices and set slices on paper towels. Sprinkle lemon slices with sugar.
In a small bowl, stir together the crumb ingredients and cut in cold butter pieces. The mixture should be chunky and the butter should be in pea-sized pieces.
In a stand mixer with the paddle attachment or a large mixing bowl with a hand mixer, cream together butter, sugar, and lemon zest. Mix until the butter mixture is light and fluffy, at least 4-5 minutes. Then beat in eggs, one at a time, and vanilla extract.
In a separate bowl, stir together dry ingredients: flour, baking powder, baking soda, and salt.
Add half of dry ingredients to the cake base, then add Greek yogurt, and finish batter with the rest of the dry ingredients.
Lightly butter an 8×8 baking dish and spread in half of the cake batter. Dot batter with lemon slices and cover with rest of the cake batter. Top with extra lemon slices and finish coffee cake with crumb.
Place coffee cake on a baking sheet to catch any that overflows and bake in a 350 degree F. oven for 55 minutes. The center should be just set.
Remove cake and let cool for 20 minutes or so and then cut into 9 even squares.