In a small bowl, mix together the lemon juice and lemon zest, the oregano, most of the olive oil and a pinch of salt. Slice up the red onion quite finely, and add to the bowl, then leave to marinate for at least 10 minutes.
Brush the remaining oil onto the burgers and cook on a griddle pan for 5 minutes each side for medium, or until done to your liking.
Lightly toast the pitta breads then make a split in each. Fill with the cucumber, tomatoes and lettuce, then slide in the burger to sit on top. Spoon over the marinated onion mixture, then crumble over the feta. Serve each filled pitta with a portion of oven chips.
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