The culinary term à la lyonnaise – in the style of Lyon – which is applied to numerous French dishes, generally means that onions are a key part of the recipe.
In Alexis Soyer's recipe (1846) the onions are fried in butter and the sliced boiled potatoes are added to the pan.
[3] August Escoffier (1907) recommends frying the potatoes and the onions separately in butter before combining them and sprinkling them with chopped parsley.
[4] Marcel Boulestin's recipe (1931) adds the onion raw to the pan in which the potatoes are frying.
She recommends either butter or beef dripping for frying both ingredients, and comments that the dish cooked in this way "bears little resemblance ... to the greasy mixture of unevenly browned potatoes and frizzled onions which usually passes for pommes lyonnaises".