Preheat the oven to 355°F (180°C).
To make the syrup, place the sugar, lemon juice, and water in a saucepan. Stir until the sugar is completely dissolved. Bring to a boil and stop stirring for 10 minutes. After 10 minutes, let the syrup cool.
Grease a rectangular Pyrex baking dish (approx. 8 x 11 inches) with butter.
In a bowl, mix the nuts, almonds, spices, and sugar. Then divide the nut mixture into three equal parts.
Brush half of a phyllo sheet with the melted butter and olive oil mixture using a silicone brush. Fold the sheet in half lengthwise and trim it so it fits the baking dish. Repeat this with three more sheets.
Tip: Phyllo dough can be a bit hard to work with. Don’t give up on the recipe for that reason! If the dough tears, you can patch the holes using trimmed pieces of phyllo dough. You won’t even notice once it’s baked—I promise!
Add one portion of the nut mixture.
Then add four more sheets of phyllo dough, brushing each with the butter-oil mixture as before.
Add the second portion of the nut mixture.
Add another four sheets of brushed phyllo dough.
Add the last portion of the nut mixture
Finish with four more sheets of brushed phyllo dough.
Brush the top with the remaining butter-oil mixture.
Cut the baklava three times across the width without cutting all the way to the bottom of the dish (i.e., don’t cut through the bottom layer of phyllo).
Bake for 30 minutes.
Pour the cooled syrup over the hot baklava.
Once completely cooled, cut into squares or diamonds.