Drain the oil from the cans of tuna into a Dutch oven with a tight fitting lid.
Add the 3 tablespoons oil and brown the veal lightly. Remove meat and set aside.
Vegetables: Add garlic, onions, carrots and celery to the oil and cook, stirring frequently, for 5 minutes or until onions are translucent.
Add parsley, bay, thyme, salt and pepper, chicken stock, tuna, the drained anchovies and two tablespoons lemon juice. Stir the mixture well to dissolve any particles that may stick to the bottom of the pot.
Bring to a boil, then add the veal. Cover and simmer for 3 hours. Remove the veal from the pot and put it in the refrigerator.
Put the pot back and reduce the vegetable-tuna mixture to about four cups, stirring time to time to prevent burning. Puree this mixture in a blender.
Add two cups of the puree to two cups of mayonnaise, 4 tablespoons of lemon juice and 2 tablespoons of capers. Refrigerate.
Before serving, slice the veal thinly and arrange the slices on a large platter with half the tuna-mayonnaise over them.
Garnish with the lemon slices and the rest of the capers. Pass rest of the sauce at the table.