Place an 8-inch square baking pan in the freezer. Puree strawberries with sugar and salt in a food processor. Add 1 1/2 cups water and lemon juice and pulse to combine. Pour through a large fine-mesh sieve set over a large glass measure or bowl, pressing hard on solids to extract as much liquid as possible. Pour mixture into cold baking pan.
Cover tightly with aluminum foil and freeze for 1 hour, or until ice crystals form around edges. Stir mixture well with a fork to incorporate ice and break up any chunks. Continue to freeze, scraping ice at edges into center and breaking up pieces with a fork every 30 minutes, for 2 1/2 to 3 hours, until granita is granular but still slightly slushy.
Use a fork to scrape across granita surface, transferring ice shards to glasses or bowls, and serve immediately, garnished with whipped cream, if desired.