However, recently I got the chance to read through every Batman Beyond series and I took copious notes to try to figure out how it should be represented on this site, and figured it out I did: there are actually three separate versions of the Batman Beyond world. In this three part post, I will describe the three versions and note the characters and concepts each one introduced. If the site has already talked about them, I'll link to that page. If not, I'll put in the new information. Here's Part 1 if you missed it; yesterday was Part 2a (Earth-12 from the Batman's side), today is Earth-12 from Justice League's side, Thursday will be Part 3, and Part 4 will be on Friday.
Version 2: The Future of Earth-12
This version provides a clean break, in that it changes its name to Batman Beyond 2.0 and Justice League 2.0. But it's more than that. Suddenly Barbara Gordon can walk again, costumes (Nightwing's in particular) reflect their animated counterparts, and they not only exclusively refer to events of the DCAU when talking about the past, they refer to the past more frequently and in deeper detail. This book does occasionally - once or twice - refer to events from previous volumes, but it does it vaguely enough that it could be talking about separate events entirely.
The Justice Lords, a dark counterpart to the Justice League from Earth-50, first appeared in the Justice League 2-parter "A Better World" (2003), the events of which are recapped in Justice League Beyond 2.0 #17 (April 2014). The Justice Lords are first mentioned in Justice League Beyond 2.0 #16 (March 2014), then appear in issue 17 in full - except for Lord Hawkgirl - but in flashback. The Justice Lords Unlimited - which include Curare - appear in Justice League Beyond 2.0 #18 (April 2014).
Jax-Ur's outfit in Superman: The Animated Series (as seen in "Blasts from the Past" (1997)), is quite different from what he wore when he first appeared in Adventure Comics #289 (August 1961), or at any other time in his history. Yet that's what he's wearing in Justice League Beyond 2.0 #4 (September 2013).
Parasite's appearance has already been discussed here, but it shows up on Earth-50 in Justice League Beyond 2.0 #18 (April 2014).
Amazo's appearance in Justice League was much more generic than his comics appearance, which debuted in The Brave and the Bold #30 (April 1960). But the generic version - specifically the upgraded gold version from "The Return" (2004) - is what's represented in Justice League Beyond 2.0 #9 (December 2013).
Brainiac's appearance isn't terribly different from his comics counterpart, but it's enough to be noticeable. You can read more about this look here, but it appeared in Justice League Beyond 2.0 #8 (November 2013).
Brainiac as Krypton's world computer is an idea that first appeared in the Superman: The Animated Series episode "The Last Son of Krypton" (1996). It was reused in Justice League Beyond 2.0 #12 (January 2014).
The merger of Brainiac and Lex Luthor, and the resulting merger of Brainiac and Darkseid happened in the Justice League Unlimited episodes "Divided We Fall" (2005) and "Alive!" (2006), respectively, and were referenced in Justice League Beyond 2.0 #11 (January 2014).
Batman and Wonder Woman's attraction was featured in several episodes of Justice League, including "Starcrossed" (2004). When Wonder Woman travelled to Earth-50, she and Lord Batman acted on it, as told in Justice League Beyond 2.0 #17 (April 2014).
Batman's Penny is a particularly clever and subtle reference. The penny itself has been around in comics almost as long as Batman has, but it comes from a one-off villain called the Penny Plunderer. In the Batman: The Animated Series episode "Almost Got 'im" (1992), Batman gets it from Two-Face, which explains why it has two heads in Justice League Beyond 2.0 #22 (June 2014).
The Justice League Watchtower - a darker version of it, at least - appears as the Justice Lords satellite on Earth-50 in Batman Beyond 2.0 #23 (June 2014). Yes, I realize this should've appeared in yesterday's post, but I forgot to write it down in my notes. It fits better here, anyway.