Purée the watermelon in a food processor or blender. Add the sugar and process for 30 seconds.
Pour into a saucepan and bring slowly to the boil, stirring until the sugar has dissolved, then simmer for 1 minute. Remove from the heat, add the lemon juice, then leave to cool, adding a few drops of pink food colouring, if liked. Chill for at least 1 hour or overnight.
Use an ice-cream machine for the best results. Half-freeze the mixture according to the manufacturer's instructions, then lightly whisk the egg white and add with the motor running still running. Stir in the chocolate chips, then transfer to a plastic freezerproof container and freeze until firm.
Alternatively, freeze the mixture in a shallow freezer tray until frozen around the edges, then mash well with a fork. Whisk the egg white until stiff in a bowl. Drop spoonfuls of the sorbet into the egg white while whisking constantly with a hand-held electric whisk until the mixture is thick and foamy. Return to the freezer to firm up, then stir in the chocolate chips when almost frozen. Freeze until firm.
Transfer the sorbet to the refrigerator for 20 minutes before serving to soften. Serve with dessert biscuits.