Combine fish and 1/2 cup lime juice in a stainless steel or glass bowl. Cover and refrigerate 30 minutes. (The fish will overcure and have a mushy texture if you exceed 30 minutes.) Drain and discard juice.
Stir in onion and next 10 ingredients. Cover and refrigerate 1 hour or overnight. Serve in chilled glasses or on lettuce-lined plates, and garnish, if desired.