Process the zest, sugar and salt in a food processor until damp, ten to fifteen 1-second pulses. With the machine running, add the orange juice and lemon juice in a slow, steady stream; continue to process until the sugar is fully dissolved, about 1 minute. Strain the mixture through a fine-mesh strainer into a medium bowl. Stir in the Triple Sec, then cover with plastic wrap and chill in the freezer until the mixture reaches 40 degrees F, about 30 to 60 minutes. Do not let the mixture freeze.
When the mixture is cold, whip the cream in a large bowl until soft peaks form. Continue to whip constantly and add the juice mixture in a slow, steady stream, pouring against the edge of the bowl.
Immediately start the ice cream machine and add the orange mixture to the canister; churn according to the manufacturer directions. When done, the sherbet should have the consistency of soft-serve ice cream. Transfer the sherbet to a freezer-safe container and freeze until firm, about 3 hours.