Pineapple Anise Sherbet

Bring water, sugar, and anise seeds to a boil in a 2 1/2- to 3-quart heavy saucepan, stirring until sugar is dissolved, then reduce heat and simmer, uncovered, 5 minutes.

Remove pan from heat and stir in Pernod (if using). Cool syrup to room temperature, about 1 hour, then pour through a fine-mesh sieve into a bowl.

While syrup cools, cut enough pineapple into 1-inch chunks to measure 5 1/4 cups (reserve remainder for another use), then purée pineapple in 3 batches in a blender at high speed until very smooth, about 1 minute per batch. Stir purée and lemon juice into cooled syrup until combined well, then chill, covered, until very cold, about 4 hours.

Freeze in ice cream maker, then transfer to an airtight container and put in freezer to harden, at least 1 hour.

Sherbet can be made 3 days ahead.

Let soften slightly before serving.