https://www.reddit.com/r/DC_Cinematic/comments/1t2ig0b/in_the_snyderverse_lex_luthor_was_clearly_an/
In this particular case, fans didn't use huge irrefutable facts but that's still a good thing. Because valid arguments were used in a genuine and honest way. With respect. Kudos to them. I really love how you turned the table by transforming this post into a DCEU's Luthor appreciation post. To point the details that you liked about this character.
This redditor (who also posted the question here) is probably overthinking. He also forget that in the DCEU, Metropolis and Gotham are close and Arkham is probably considered to be better suited and more effective than Metropolis asylums (remember that Batman is active since 20 years, so Arkham might be truly better for insane super-villains and murderer and very dangerous being like Lex). At least, this is maybe what Batman used as fake arguments to transfer him into Gotham. So he isn't really an anomaly.
Also, my memory is bad but didn't Lex comitted crimes in Gotham too? So it was also easier for Batman to convince his relationship from the justice and medical department. Lex killed way too much people during the events of BvS, so some people were probably glad to see Bruce Wayne asking personnally to them, to put him in Arkham.