We shouldn't put too much weight on the statements of the Lazarus from our universe. That is, we should put zero weight on them. He's lying, plain and simple. About everything.
Likely lies (that is, a list of times his lips were moving):
- "My planet was in location X" (a lie Kirk later challenges him on, so he told this lie at one point even if we didn't hear it)
- "I chased the monster across the universe"
- "He murdered my civilization"
- "I was saved because I was inspecting a magnetic satellite" (as why tell the truth here when everything else is a lie?)
- "The planet below is my Earth"
- "I am a time traveler and so is he"
As far as I can tell, the less insane Lazarus, from the other reality that initiated the connection, never makes nor supports any of the above claims. Nor do the claims make much sense, even if we assume that the saner Lazarus is lying about some things as well. And since there is no rhyme or reason to the lies, we should assume the insane Lazarus simply lies for the sake of lying.
Timo Saloniemi