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1
Process zest, sugar, and salt in a food processor until damp, ten to fifteen 1-second pulses.
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2
With the machine running, add lemon juice and water in a slow steady stream; continue to process until the sugar is fully dissolved, about 1 minute.
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3
Strain the mixture through a non-reactive fine-mesh strainer into a medium bowl to remove pulp and zest; stir in Triple Sec, then cover with plastic wrap and chill in the freezer until very cold, about 40u00b0, 30-60 minutes (Alternatively, set the bowl over larger bowl containing ice water).
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4
Do not let mixture freeze.
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5
When mixture is cold, using a whisk, whip the cream in a chilled medium bowl until soft peaks form. Whisking constantly, add the chilled juice mixture in a steady stream, pouring against the edge of the bowl.
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6
Immediately start the ice cream machine and add the juice/cream mixture to the frozen insert.
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7
Churn until the sherbet has the texture of soft-serve ice cream, 25 to 30 minutes.
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8
Remove the canister from the machine and transfer the sherbet to a storage container; press plastic wrap directly against the surface of the sherbet (to prevent ice crystals from forming) and freeze until firm, at least 3 hours. Can be wrapped well in plastic and frozen for up to one week.
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9
To serve, let sherbet stand at room temperature until slightly softened and an instant-read thermometer inserted into the sherbet registers 12u00b0 to 15u00b0.
