Make pudding cake: Preheat oven to 350 degrees F.
Whisk together flour, salt, and 1/2 cup sugar in a bowl. Whisk together yolks, milk, zest, and juice and add to dry ingredients, whisking until combined well.
Beat whites in a large bowl with an electric mixer until they hold soft peaks, then gradually add remaining 1/4 cup sugar, beating, and continue to beat until whites hold stiff, glossy peaks. Whisk about one-fourth of whites into batter to lighten, then fold in remaining whites gently but thoroughly (batter will be thin).
Pour batter into a lightly oiled 1 1/2-quart gratin or other shallow baking dish and bake in a hot water bath until puffed and golden, 40 to 45 minutes.
Make raspberry coulis while cake is baking: Puree raspberries with syrup, sugar, and lemon juice in a blender or food processor. Pour mixture through a fine sieve into a bowl, pressing on solids.
Serve pudding cake with syrup.
Notes: Coulis keeps 3 days, covered and chilled. You can also make this coulis with fresh raspberries. The amounts will be slightly different: Use 2 1/2 cups fresh raspberries and 1/4 cup sugar.