Preheat oven to 350ºF. Line baking sheet with parchment; set aside.
In a food processor fitted with metal blade, combine artichoke hearts, leeks, garlic cloves and lemon juice. Pulse several times or until ingredients are finely chopped. Add mayonnaise and sour cream; process until well combined, stir in Parmesan cheese and chives.
Fill each mini filo shell with filling and place on prepared baking sheet. Bake in preheated oven until heated through and golden brown, about 30 minutes.