Purée watermelon in a blender until smooth, then pour through a fine-mesh sieve into a 2-quart saucepan, pressing on pulp and then discarding any remaining solids.
Ladle about 1/4 cup watermelon juice into a small bowl and stir in cornstarch until smooth.
Bring remaining watermelon juice to a boil with 1/2 cup sugar and anise seeds, stirring until sugar is dissolved. Stir cornstarch mixture again, then whisk into boiling juice. Reduce heat and simmer, whisking occasionally, 3 minutes. Whisk in lemon juice.
Pour pudding through cleaned sieve into a bowl, then transfer to a wide 1-quart serving dish or 6 (2/3-cup) ramekins and chill, uncovered, until cold, about 30 minutes. Cover loosely and chill until set, at least 3 hours.
Just before serving, beat cream with the remaining 1 teaspoon sugar in another bowl with an electric mixer until it just holds stiff peaks. Top pudding with whipped cream.
