Follow the steps in order for the best result.
Begin by zesting the lemon, ensuring the zest is finely chopped. Then, extract the juice from the lemon and set both aside.
In a small saucepan, combine the sugar, half-and-half, and lemon zest. Heat the mixture over medium heat, stirring constantly, until the sugar is completely dissolved. Be careful not to let it boil. Once the sugar is dissolved, remove the saucepan from the heat and allow the mixture to cool to room temperature.
Once the sugar mixture has cooled, incorporate the lemon juice, crushed pineapple, and all of the pineapple juice from the can into the mixture. Stir well to combine all the ingredients.
Pour the combined mixture into a freezer-safe container and freeze until it is partially frozen, about an inch or so from the edge.
Using a spoon, transfer the partially frozen mixture into a mixing bowl. Use an electric mixer to beat the mixture until it is smooth and creamy.
Gently fold in the whipping cream, ensuring it is evenly distributed throughout the sherbet mixture.
Spoon the sherbet back into the freezer trays or container. Freeze again until partially frozen. Beat the sherbet again, then refreeze until solid before serving. This step helps to create a smoother, less icy texture.