With a zester, remove strips of zest from 4 of the tangerines. Set aside. Extract the juice from all 8 tangerines. (There should be about 3 cups of juice.)
Combine the tangerine zest, sugar, and 1 cup water in a medium-size saucepan and bring to a boil over high heat. Reduce the heat to medium-low and simmer until the syrup is reduced to 1 cup, about 20 minutes. Remove from the heat and let cool.
Drain the syrup into a large bowl, reserving the candied zest for garnish. Stir the tangerine juice and lemon juice into the syrup. Cover and refrigerate until well chilled (or chill over a bowl of ice water, stirring the mixture occasionally).Freeze the mixture in an ice cream maker according to manufacturer's instructions. If not transfer the sorbet to a plastic container. To prevent ice crystals from forming, place a piece of plastic wrap directly on the surface of the sorbet before putting the lid on the container. Store in the freezer.
If not using an ice cream maker, place the chilled mixture in a stainless steel or other metal baking pan, cover with plastic wrap, and freeze until softly set, about 2 hours. Transfer the partially frozen mixture to a food processor and process until smooth and fluffy, about 10 seconds. Return the mixture to the baking pan, freeze until half-set, and repeat the process. After the second blending, transfer it to a plastic container. To prevent ice crystals from forming, place a piece of plastic wrap directly on the surface of the sorbet before putting the lid on the container. Store in the freezer until the sorbet is solid, about 4 hours.
Remove the sorbet from the freezer 10 minutes before serving. Serve in chilled stemmed glasses. Garnish each serving with the reserved candied tangerine zest and a mint sprig, if desired.