Lightly brush a 4-cup soufflé dish with oil. Fold a 2-foot-long piece of foil in half lengthwise and wrap it around the outside of the soufflé dish to form a collar. Secure the collar with tape and lightly brush the inside with oil.
In a small bowl, sprinkle the gelatin over the water and let stand until softened, about 5 minutes. In a heavy medium saucepan, whisk the egg yolks with the lime juice, 1/2 cup of the sugar and the salt. Cook over moderately low heat, whisking constantly, until boiling and thickened, about 5 minutes. Remove from the heat, add the gelatin and whisk until dissolved. Add the lime zest and transfer to a large bowl to cool.
Using a handheld electric mixer, beat the egg whites at medium speed until soft peaks form. Gradually beat in the remaining 1/2 cup of sugar until stiff.
In a large bowl, whip the cream until stiff peaks form. Fold the beaten whites into the whipped cream. Stir one-third of this mixture into the lime custard, then fold in the rest. Spoon the soufflé mixture into the prepared dish and smooth the top.
Freeze the soufflé until firm, at least 4 hours, or wrap it well and freeze for up to 2 days. Serve the soufflé with fresh berries and diced mango.