You don't see how two ambitious and power hungry people doing whatever it takes to save the world while putting themselves ontop could work? Because I can. The two aren't anti one another. You can nurture a power base while stopping a greater threat (especially since that threat itself threatens you and your power as well).
Again I'm not looking for stupid evil kick the puppies as they walk by types. Someone who wants to expand their own influence and wealth and a villian with great publicity is the type of evil I'm looking for. Someone who's not at all unwilling to crack a skull open if something they need is inside it but they won't just do it for the evilulz if it's unnecessary since they're well aware a good reputation is helpful and being loved is better than being hated.
Reading through much of the thread, I think it would help to identify that horribly divergent question of 'what is evil?' Or rather, 'what is evil enough'?
Are we looking for someone who simply has very significant character or moral flaws? Someone who advances a cause that harms others? Someone who is unapologetic about flouting certain social conventions? Someone who holds cultural beliefs radically different in values from modern western liberalism?
There's quite a bit you could do with all of them, enough so that I think fixating on 'evil' is a bit misleading. Evil frequently implies a malevolence that need not apply: David Xanatos was unquestionably an antagonistic villain, but he was more about amoral self-interest than making people suffer for laughs. He also had a close friend and an honest romantic relationship.
Since a LI should be attractive or appealing in their own right, even if they aren't of full moral rectitude, I think focusing on 'evil' LI's is a misnomer.
I need to get some sleep for tomorrow, but here's some ideas that I'll try to elaborate more on later that could be legitimate LI 'flaws' that needn't overshadow the character to the point of utter unlikability.
1. Imperialist administrator/aristocrat.
2. Casual racism.
3. Cultural chavenism.
4. Ideological Zealot
5. Unrepentent petty criminal (especially scam artists)
6. Corrupt official/white collar criminal
7. Amoral ego-centric (a particularly good one: they care more about your perception of them than anything they do in partiuclar)
8. Petty rivalries with others
9. Deliberate corruptor
And, of course...
Yandere