Discosoma vs Lobophyllia
I think the lobo will win. I have similar experience with lobo stinging my merulina (not sure spell correctly) - the merulina was badly injured, exactly the thread like stuff you have shown comes from the lobo.
But I noticed something interesting - frogspawn has no effect on Lobophyllia and even the frogspawn doesn't sting the lobo too. Not sure if others have the same experience.