Combine dates, sugar, water, lemon juice, and marshmallows in a medium saucepan; cook over medium heat, stirring frequently, until marshmallows melt. Set aside to cool.
Combine butter and cream cheese in a medium mixing bowl; beat until smooth. Add flour and salt; mixing well. Shape dough into a ball; chill 20 minutes.
Roll pastry to 1/8-inch thickness on a lightly floured surface; cut into 4-inch squares. Place one tablespoon date mixture in center of each square. Moisten edges of pastry with water; fold squares in half to form a triangle. Press edges together with a fork to seal.
Place turnovers on an ungreased baking sheet. Bake at 400° for 15 minutes or until lightly browned.