Arrowverse league of assassins is best live tv version of the organization.
Honestly most live dc stuff doesnt hold a candle to the DCAU in terms of writing, character development, and comicbook accuracy.
The plot of one movie was
Owlman playing the crime syndicate to his goals of blowing up the entire multiverse as he concluded universal suicide is the only act worth meaning in the infinite flow of time and space as every other action has been done before in one existence or another
Even the awesome marvel movies dont get that deep with character motivations.