Make a simple syrup with water and sugar. Bring them to a boil in a small pot. Let simmer for 3 minutes until the sugar has dissolved. COOL COMPLETELY.

While it is cooling. Add raspberries (thawed will make this easier)and lime juice in a processor or blender like a Ninja and puree.

Strain the pureee through a strainer to remove seeds. Not mandatory but there are a ton of seeds in there.

Combine the puree, simple syrup, and corn syrup in a large bowl. If you have clumps in your puree a quick whisk will remove them.

Scoop or pour mixture into ice cream maker and freeze as instructed in manual. It takes about 25-30 minutes usually. Note that it will be soft almost slushy like when it comes out, it will harden up in the freezer. If you want it to be harder freeze for at least two hours before serving, overnight is best.