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So I read that the initial lion and wolf dual didn't end with Jonson or Russ' death but are the duels held by the chapter (Space Wolf and Dark Angel) champions a fight to the death or is it just a sparring match for bragging rights?

It isn't a fight to the death it is a fight for bragging rights...
Though apparently the Lion and Russ eventually became friends.

Yeah, it's a ceremonial thing- a (more or less) friendly rivalry.

Although in some of the fluff, the 'rivalry' is actually a deep distrust between the two chapters. An example would be the Ragnar series of books from BL where DA and SW engage in an all out war on the surface of a planet because the DA don't tell the SW about the Fallen they are looking for.