Drain the tuna fish and anchovies and place them in a blender. Add most of the capers, along with their juice, add the lemon juice and blend until smooth. Add the mayonnaise and blend again until fully combined. The consistency should be similar to a white sauce - smooth and thick but just pourable. If it needs more liquid, add a little more mayonnaise and a drop of milk.
Place your cold sliced meat (veal, turkey, pork etc,) on a large serving dish and coat with the sauce, using the remaining capers to garnish over the top.