Wash and dry the lemons. Using a sharp knife, slice off the top third of each lemon (the stem end). Set the tops aside for another use or discard.

Using a small knife and a spoon, carefully scoop out the lemon flesh, leaving the white pith intact to form a sturdy cup. Reserve all the lemon flesh and juice. You should have about 1 cup (240ml) of lemon juice. If short, squeeze the extra lemon.

Strain the lemon juice through a fine-mesh strainer into a liquid measuring cup. Discard seeds and pulp.

In a small saucepan, combine the sugar, water, and salt. Warm over medium heat, stirring gently, until the sugar is fully dissolved and the syrup is clear. Do not boil. Remove from heat and let cool to room temperature, about 10 minutes.

In a medium bowl, whisk together the cooled syrup and the strained lemon juice. If using the egg white, whisk it in now until fully incorporated and slightly frothy. This helps create a creamier, less icy sorbet.

Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency, about 20–25 minutes. If you don't have an ice cream maker, see the note below.

While the sorbet churns, place the hollowed lemon cups in a small baking dish or on a tray that fits in your freezer. This keeps them upright and stable.

Once churned, spoon the soft sorbet into each lemon cup, mounding it slightly. Work quickly so the sorbet doesn't melt.

Transfer the filled lemon cups to the freezer and freeze for at least 4 hours, or until firm. For best texture, let them sit at room temperature for 5 minutes before serving.