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Preheat the oven to 350°F with a rack in the center. Line a 9" x 13" pan with parchment. Grease the parchment with butter or nonstick spray.
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In a medium bowl, whisk the semolina, coconut, baking powder, and salt to combine.
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In a large bowl, whisk the melted butter or ghee and sugar to combine. Add the yogurt, eggs, and vanilla; whisk to combine. Add the dry ingredients and mix with a flexible spatula until just incorporated. The batter will be thick.
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Transfer the batter to the prepared pan and use an offset spatula to spread it into an even layer. Use a thin knife to score the batter about 1/8" deep in a 3 x 4 pattern to make 12 squares. Score the squares diagonally to make 24 triangles. Use these score marks as a guide for placing one almond in the center of each triangle.
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Bake the basbousa for 30 to 35 minutes, or until light golden brown all over.
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Toward the end of baking, prepare the syrup. In a small pot, combine the water, sugar, and lemon juice. Cook over medium heat, stirring often, until the sugar has dissolved and the syrup begins to simmer, 4 to 8 minutes.
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Pour all of the syrup slowly and evenly over the hot cake, pausing as needed to allow it to soak in before adding more. Let the soaked cake cool completely in the pan on a wire rack.
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Once cooled, use the score marks to cut the basbousa into 24 pieces and serve at room temperature.
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Store leftover basbousa in an airtight container at room temperature for up to 5 days.
