If using fresh fruit, dice into small pieces and freeze for at least 2 hours or overnight.
Add frozen fruit to a food processor or high-powered blender.
Pulse the fruit 8-10 times to break it into small chunks.
With the processor running, gradually drizzle in 3 tablespoons of your chosen sweetener.
Continue processing until the mixture reaches a smooth, sorbet-like consistency, about 2-3 minutes.
Taste and add additional sweetener if needed.
Add lemon or lime juice for extra brightness if desired and pulse briefly to combine.
Serve immediately for a soft-serve texture, or transfer to freezer for 15-30 minutes for a firmer consistency.