Purée raspberries (with juice) with salt, vanilla and lime juice. Strain out and discard seeds. Reserve purée in a deep, narrow container. Refrigerate. Mix together sugar and water in a saucepan and bring to a boil. Boil 1 minute and remove from heat. Cool.
If you have a Baumé hydrometer, look for a reading of 120-140 in your raspberry mixture. If you do not have one, wash a fresh egg with soap and water, rinse and dry (very important to clean off bacteria!). Place it in raspberry purée and slowly add sugar syrup, stirring gently. When the egg floats until a dime-sized portion of it is visible on the surface, you have reached the correct Baumé measurement of density.
Chill mixture for at least 4 hours. Churn in an ice cream machine, as per manfacturer’s instructions. Serves 8.