I don't think (any) alliances do comp - some (individual) airlines (best bets are the NorthAmerican ones) do.
LH, in my experience doesn't (they didn't comp me, even when their partner UA gave up their only flight into Switzerland in 98: IAD-ZRH), Mr Fuchs (heading UA Austria/Germany/Switzerland still now) did even write a recommendation letter than to LH to comp me, but LH declined then ...