Grease and flour a 9" springform pan. Put 2 lemons in a medium pot and cover with water by at least 2"...although, honestly, the lemons will float....but make the depth of water 2" deeper than the height of the lemons. Bring to a boil, reduce to simmer, partially cover pot, and let simmer for 40 minutes or very tender. Mine had kind of collapsed in on themselves.

Use a slotted spoon to transfer lemons to a cutting board. Let cool. Use a spoon to break into the lemons and remove the pits. Purée lemons in a food processor or blender, scraping down the sides frequently.

Heat oven to 350º. Zest most of remaining lemon into a medium bowl. (Save a bit of the zest, and the rest of the lemon for the glaze.) Stir in almond meal, flour, baking powder and salt.

Using an electric mixer, beat egg whites until very foamy. With the mixer still going gradually beat in ¼ c. sugar, continuing to beat until stiff peaks form. Slide beaten whites into a large measuring cup or bowl.

In the same mixing bowl (you don't need to wipe it out) beat egg yolks and remaining 1 c. sugar until thick and pale, about 1 minute. Beat in lemon purée, almond meal mixture, and almond extract. Using a rubber spatula, fold in melted butter and olive oil.

Fold a third of the egg whites at a time into the cake batter, taking care not to over mix. Spread batter into prepared springform pan.

Bake until top of cake wis well browned and it springs back when lightly pressed in the center, 45-60 minutes. (Mine took about 50 minutes using a convection oven.) Transfer to a wire rack to cool.

When cake has mostly cooled, about 30 minutes later, make the glaze. Zest the remaining part of the last lemon, and then juice it, being sure to strain out the seeds. Stir the confectioners' sugar into the zest and juice, until you have a thick, but pourable glaze. If you baked your cake in a springform plan, you might want to be sure to put a plate under it at this point, as some of the glaze leaked out of the bottom edge of my pan, and onto the counter below since I left it on the wire rack. If your glaze is too thin, add more sugar. If it's too thick, add a bit of water. Pour glaze over slightly warm cake and let cool completely.