Puree the raspberries with a food processor or smoothie maker to a very fine puree.
Bring the raspberry puree and erytrith to a simmer in a small saucepan, stirring constantly until the erytrith has dissolved. Put the mixture in the refrigerator and let it cool.
Pass the puree through a fine sieve. This works best with a spoon. You don't have to put the whole puree through the sieve. Half of it is enough. A few seeds are perfectly ok.
Add the lime juice. Grate the zest from the lime and add the zest.
Whip the cream until stiff and fold it into the puree.
Put it in the ice cream maker. After about 30 minutes, the raspberry ice cream is ready.