During their fight the Justice Lord Superman and Doomsday punch each other simultaneously. In the comics, this is what resulted in both of their deaths during the Death Of Superman story-line.
The Lord J'onn's alibi about dimensions collapsing on one another was actually the plot of a miniseries Crisis on Infinite Earths; the part heard in the background when Batman and J'onn talk amongst themselves is "Perhaps by combining our forces, we may be able to avert this crisis which threatens all the infinite Earths and all the divergent time-streams," which was what was done in the story after all the universes merged into one.
The Justice Lords were originally planned to be the Crime Syndicate, an alternate dimension version of the JL featuring evil doubles. However, as the scripting went on, the plot changed so much that the writers decided to replace them with The Justice Lords. The Crime Syndicate were planned to appear in a DTV movie, Justice League: Worlds Collide, but the production was canceled just before the start of filming. However, the original script script was recycled into the DC Animated movie Justice League: Crisis on Two Earths (2010).
The reason the alternate Flash is stated to have died is because the writers couldn't think of how to present a version of him as evil.
According to the Season 2 DVD, the Justice Lords' suits were left over from plans when Bruce Timm had led discussions giving the Justice League wearing uniform outfits, but could not get the DC Comics president to allow it for Batman, Superman, or Wonder Woman, which resulted in its being dropped. Lorder Wonder Woman's is similar to the original one for Teen Titans member Wonder Girl/Donna Troy's of the original Teen Titans. Justice Lord Superman's costume resembles the costume originally worn by the Eradiactor during the "Reign of Supermen" comic series; during which four "imposter" Supermen appeared in the wake of Superman's death at the hands of Doomsday (who also makes an appearance here). The Eradiactor was one of these men who, like the Justice Lord, killed criminals. The insignia worn by Lord J'onn is similar to that worn by Marvel Comic's Dr Strange.