Prepare an ice bath in the sink or in a large heatproof bowl.
In a medium saucepan, combine the lemon juice, sugar, corn syrup, egg whites, ginger puree, and 2 ½ cups (600 ml) water. Whisk vigorously until smooth.
Clip a candy thermometer to the saucepan and set the pan over medium heat. Cook, stirring regularly, until the mixture reaches 165°F (75°C). Transfer the pan to the prepared ice bath and let cool for 15 to 20 minutes. Stir in the limoncello. Pour the sorbet base through a wire-mesh strainer into a storage container and place in the refrigerator for 1 to 2 hours, or until completely cool.
Transfer the cooled base to an ice cream maker and churn it according to the manufacturer's instructions.
Transfer the sorbet to a storage container. Serve immediately or harden in your freezer for 8 to 12 hours for a more scoopable sorbet.