In a large pot, cook the onion, garlic, and spinach in the olive oil until the spinach is limp and the liquid has reduced. Add the lemon juice, rosemary, salt, and chevre. Mix well.
Cut fila in half crosswise, then cover loosely to keep from drying out. With a pastry brush, coat bottom of a 9 x 13 pan with butter. Line pan with a sheet of fila. Brush fila lightly in a few places with melted butter. Cover with another sheet of fila and brush lightly with butter. Repeat until you have used half the fila.
Spread cheese and spinach mixture evenly over fila. Cover with another sheet of fila and brush lightly with butter, repeat with remaining fila. Brush top with remaining butter. (At this point, you may cover and refrigerate until next day)
Bake, uncovered, in a 375 F oven for 35 minutes or until top of pastry is golden and crisp.