If you don’t have a close relationship with your butcher, you must clean the lung quite thoroughly yourself.
Chop 1 onion fine, add 1 bay leaf, and cover with water. Cook for 30 minutes. Add heart and cook for about 30 minutes, then add lung and cook for about 30 minutes longer, until both are tender.
Remove the cooked meat from the water and cut it into very fine strips. Place strips in a cooking-serving casserole. Reserve the cooking liquid.
Chop the other 2 onions and the garlic till the pieces are very fine. Grate the rind of the lemon. Mix onions and garlic, lemon rind, capers and minced anchovies, gherkin, tarragon and parsley.
Melt lard. Crush and dissolve the sugar cubes in it. Add the flour. Stir constantly over very low heat while browning this roux.
Add the mixture assembled in step 4 plus the remaining 2 bay leaves to the roux. Again stir constantly with a wooden spoon over low heat for another 3 or 4 minutes.
Add ¼cup cold water to the thickened mixture and vigorously whip it. Then add about 1cup of the liquid in which the lung was cooked; use as much as needed to make a heavy, creamlike sauce. Bring to a boil.
Adjust the flavor of the sauce with lemon juice, mustard, vinegar and salt to taste. The sauce can be sharp or sweet or piquant according to the way you adjust the taste at this point. Pour the sauce over the meat strips in the casserole, bring it to a boil, and serve. If you like, sprinkle the top with Paprika Essence and minced parsley.