The "lobotomized" inmates in the Justice Lord universe Arkham Asylum include Two-Face, The Penguin, The Riddler, and The Ventriloquist and Scarface. All of the inmates have scars on their foreheads as the result of being lobotomized by Superman's heat vision--except for The Ventriloquist. The dummy Scarface has the "scars" on his forehead instead.
According to Bruce Timm, the lines uttered by Justice Lord Superman's robotic replicas are unpopular quotes spoken by Superman in the first season of Justice League. The gag was episode writer Stan Berkowitz's idea.
For the dialogue between Batman and Lord Batman, Kevin Conroy conversed with himself, speaking both separate character's responses to each other as one single line.
Batman the Justice Lord has the ears on his costume inverted from the position that Batman wears his. Batman's ears point like shark fins facing forward, while Lord Batman's are backwards.
Batman's and his Justice Lord's counterpart's argument dialogue was deliberately worded by the writers so, if unseen, it would be ambiguous whom speaks which line regarding how his world better served justice. Batman temporarily yields to Lord Batman's argument about how the Lords' fascist rule is superior because the writers couldn't immediately think of a counterargument. Later they were able to, which is why he quips about the world's shortcomings a few scenes later.