Quick Summation: Doctor Light uses his powers to mix up the leaguers secret identities. Why he does this, I'll touch on in a second, but crux of his scheme gives us the issues title:
For one, amnesia (or mind wiping) is a main plot device:
Anyway, also just like in Identity Crisis, there is a "death" in this issue. In this case it's Aquaman, who meets his end when he accidentally touches booby trapped luminescent fish.
Here is the scene in JLA 122 that I think inspired IC's angry Batman attack:
I suspect this scene was the inspiration for how Jean Loring killed Sue Dibney in Identity Crisis by jumping on her brain.
What all of the connections have in common I believe is the older JLA 122 versions probably deeply affected young Brad Meltzer in a way that stuck with him. I'm sure we all have scenes from old comics that we remember reading when from our youth that rocked our world as kids. In Brad's case, he was able to take some of that youthful anxiety and increase it in a way that was effective on adults. (In some cases too effective.)
There are many people who do not like Identity Crisis for a number of reasons, (like Grant Morrison, who takes great offense with the Sue Dibney rape scene.) And while I think it definitely has its flaws, the mini-series does indeed find a way to take some of the elements from Bronze age stories and make them more provocative and interesting for an older audience.
The real question is: Is that a good thing?