Start by zesting the limes, set aside. Now juice the limes, orange, and lemons. Strain, and measure out 1 ⅓ cups of fresh juice (combine ¾ cup fresh lime juice, ¼ cup fresh orange juice, and ⅓ cup fresh lemon juice) and refrigerate.
Make a simple syrup by combining the sugar and water in a small saucepan over medium heat. Stir and cook until the sugar has dissolved, remove from heat, and when cool enough to handle, transfer to a jar and refrigerate until cool.
Combine the citrus juice, simple syrup, and yogurt in a medium bowl. Mix, using a hand blender, until smooth.
Freeze using manufacturer’s instructions in an ice-cream maker, adding the salt and lime zest when the sherbet is the consistency of thick frosting. Serve or transfer to a freezer immediately.
