Combine salt and water in a large bowl. Spread half of the salt mixture into a large rectangular shape on a jellyroll pan. Place whole fish on top of salt; insert rosemary sprigs and lemon slices into cavity of fish. Pat remaining salt mixture over fish to cover completely. Bake at 450° for 30 minutes.
Tap edge of salt with a knife to loosen; lift salt off fish. Serve with lemon wedges and drizzle with extra-virgin olive oil, if desired.