Bring tripe, 2/3 of the juice of one lemon, olive oil, garlic cloves, salt and water to a boil in a large saucepan. Cover and simmer on low heat for about 1 hour. Add water if necessary to keep the tripe covered. Skim off any foam.
Remove the tripe from the cooking pot and cool. Keep the above mass of cooking liquid.
In another saucepan, heat the butter. Stir in the flour and saute for 2 min over medium heat until soft. Slowly add the milk, stirring throughout, as well as the clear soup, then the tripe. Simmer gently for about half an hour, stirring frequently.
Stir through vinegar, Turkish paprika and remaining garlic in a small baking bowl. Divide soup evenly into plates and drizzle with a tiny bit of vinegar mixture.