Combine eschalots, both vinegars, salt and pepper in a mixing bowl and stand 30 minutes. Add anchovies, olives, lemon zest, thyme, parsley and olive oil. Check seasoning and adjust if necessary.
Place flour and whisked eggs in separate shallow bowls. Combine thyme, breadcrumbs, seasoning and parmesan in another shallow bowl.
Dust lamb cutlets with flour, shaking off excess, then dip in eggs and coat in breadcrumb mixture, pressing mixture to ensure that it sticks.
Heat oil in a large frying pan over medium-high heat.
Cook lamb, in batches, for 4-6 minutes, or until golden brown and medium-rare, turning halfway. Drain on paper towel.
Serve cutlets with a bowl of the salsa to share at the table.