Hmm... The classic Evil Twin concept probably deserves another novel method of introducing both the Twin, and the manner in which the Twin can be mistaken for his less evil counterpart. This episode didn't really provide any - but if it had pulled its act together and explained to the audience (via pretty VFX) how one Lazarus suddenly becomes the other in the middle of the action, switching from noble motivations to evil ones, this story would have earned its place in any scifi context.
In such a case, the conclusion of our main hero Kirk figuring it out and freeing the two of this devilish curse of alternation and instead allowing them to confront each other directly would have been satisfactory enough. The meat of the episode would have come from a more careful exploration of the good and evil ways the Lazari use in their own attempts, while the "if they meet in uncontrolled circumstances, horrible things will happen" thing could have been kept as is, forcing Kirk to be clever somehow.
(It's not as if the technobabble would really need changing, though. Our heroes speak of these two universes by comparing them to matter and antimatter, but the comparison need not be exact; "antimatter universe" could be a practical if inaccurate expression for something vastly more alien.)