Heat vegetable oil in a large saucepan over medium heat. Slowly cook and stir onions until softened. Add minced garlic and cook one minute more.
Mix in the thoroughly drained spinach and dill. Sprinkle flour over the top and stir to combine. Cook approximately 5 minutes, or until most of the moisture has been absorbed. Remove from heat.
Zest the lemon and add zest to the spinach mixture. Squeeze the juice from the zested lemon halves into the mixture as well.
In a separate bowl, mix feta, eggs, and seasonings. Add the feta mixture to the warm spinach mixture and stir to combine.
Spray the bottom of a 9 x 13-inch baking dish with cooking spray. Lay one sheet of phyllo dough flat in pan.
Dip a pastry brush 1/2" or less into the melted butter: you don't want to overload it. Brush the single sheet of phyllo dough at the bottom of the baking dish with a little butter. Do not dip the brush in the butter more than once - you don't need to completely cover each pastry sheet with butter. (I can usually do at least two sheets with one brush dip.)
Add another sheet and repeat until you have five sheets total.
Spread 1/2 of spinach mixture over the buttered phyllo dough layers.
Layer on 5 more sheets of phyllo, buttering lightly in between each layer. Spread on remaining spinach mixture.
Top with the last 5 sheets of phyllo, buttering lightly between each layer.
Bake in the preheated oven 45-50 minutes, or until golden brown.