The actual Comic storyline answers that for you. Lex's New Legion of Doom has absolutely nothing to do with any previous versions. And in the storyline a lot of villains either turned them down or stood against them. The original (your) Legion of Doom wanted to rule the world. Lex's Legion of Doom wants to bring forth Perpetua to remake the Multiverse, killing Hero and Villain alike. (Well actually transforming everyone into mindless slaves of Perpetua but same difference) If you want to help Lex you'd literally be doing it to try and make sure Perpetua deletes your Villain.