Wikipedia article on the episode. It is clear to me that the Lazarus from the normal universe wanted to meet the Lazarus from the anti-matter universe, and if that would happen both universes would be destroyed. The good Lazarus (from the anti-matter universe) asked Kirk to help him trap Lazarus in the corridor with him. Under what circumstances would both universes be obliterated? Is it if both Lazaruses were in the same universe outside of the corridor? I don't understand why they needed to be locked in the corridor forever. Why couldn't one be destroyed or the bad one be imprisoned so he could never go to the other universe? I also don't understand how both doors were destroyed: the Enterprise only shot at Lazarus' ship in one universe, isn't there still the other one?
Also towards the end Captain Kirk says to Lazarus "You'll be trapped inside that corridor with him forever. At each other's throats throughout time". Can't one kill the other in the corridor?