In a blender, place the beets and juice from the borscht jar, sugar, pineapple, and lime. Blend on high for 2-3 minutes. Strain into a 9x13 baking dish and cover with plastic wrap. Freeze for 1 hour, scrape the granita with a fork. Repeat this process every hour for 4-5 hours, until it firms up completely. Serve as is, or layered with greek yogurt or whipped cream.

Note: you want to check on the granita every hour or so to make sure no ice crystals have formed on top.