I think you will have to bring it under cover, out of the frost at least, but keep it in a light place. When succulents get frosted the expanded ice ruptures the leaves. Outside you could try burying to pot up to the rim and putting a thick layer of mulch over it but this would probably kill off the top growth anyway so it probably wouldn't recover.

Even under mulch, a Lampranthus wouldn't be able to take a Cleveland winter. I would bring it indoors, and put it in a sunny window, in a cool room. It might even decide to bloom around March!