Vitello Tonnato's Sauce

For the sauce:

1 large egg
1/2 fat clove garlic, peeled
140 ml groundnut or other flavourless oil
1 dessertspoons white wine vinegar
40 g best-quality tuna fish in a tin or jar, drained
1 tinned anchovy fillets, drained
0,75 tablespoons salted capers, rinsed and drained
1/2 tablespoon lemon juice (or more, to taste)
salt and freshly milled black pepper

To garnish:

a few extra capers
2 tinned anchovy fillets, drained and very thinly sliced
½ lemon, sliced