Make the syrup. Combine 1/2 cup sugar and 1/2 cup water in a medium sauce pan. Bring to a simmer, stir until sugar is dissolved . Reduce heat to low and simmer 10-15 minutes, until syrup is a light golden color. Remove from heat and stir in the lemon juice. Set aside.
Meanwhile, prepare the baklava cups. Add the walnuts to a food processor and pulse until coarsely ground. Add the cinnamon, nutmeg and 1 tablespoon of sugar, pulse a few times to combine. Pour in the butter, pulse 2-3 more times to mix. The walnuts should be about the same texture as breadcrumbs - not too finely ground.
Place the phyllo cups in a mini muffin tin (you can also just put them on a cookie sheet if you don't have a mini muffin tin). Evenly divide the walnut filling between the phyllo cups.
Bake for 12-15 minutes, until golden. Remove from oven, and while they are still hot, spoon 1-2 teaspoons of the lemon syrup over each cup.
Best served right away, but leftovers can be stored in an airtight container.