Cut the tuna into 2 cm (approximately 3/4-inch) wide strips. Add the vegetable oil to a pan and sear sides of tuna quickly over high heat.
Chop the walnuts finely and coat the tuna strips. Peel and finely dice the shallots. In a small saucepan add the diced shallots and 1 tablespoon of olive oil. Add the vinegar and boil briefly, then add the apple juice and let simmer. After about 10 minutes, remove the pan from heat and let cool.
Meanwhile, rinse and spin dry the radicchio and lettuce. Pluck the radicchio into bite-sized pieces. Whisk the remaining olive oil with the shallot dressing and pour over the salad.
Cut the tuna crosswise into pieces and serve with the salad.