Combine 1-3/4 cups water and the sugar in a medium-sized saucepan. Bring to a boil, stirring to dissolve the sugar. Boil for 2 minutes, then remove from the heat. Stir in the lemon juice and creme de cassis. Transfer to a medium-sized bowl and let cool completely. (The syrup can be made up to 3 days in advance and refrigerated.) Puree the raspberries in a food processor, then strain through a fine-meshed sieve into the bowl containing the sugar syrup Chill until cold then process in an ice cream maker according to the manufacturers directions. (Alternatively freeze the mixture in a shallow metal cake pan or ice cube tray until almost solid. Break into chunks and process in a food processor.) Transfer the sorbet into a freezer container and freeze at least 1 hour or up to 24 hours before serving. If the sorbet has frozen solid, let it soften slightly in the refrigerator for 15 to 20 minutes before serving. Makes about 1-1/2 qts. 288 calories per cup: 1 g protein, 1 g fat, 73 g carbohydrate, 1 mg sodium; 0 mg cholesterol. dess 156