Even if you can't outright kill the Lady of Pain in your game, there is another way to defeat her that should fit 100% canonically (is that a word?).
Make her irrelevant.
Why is Sigil so important? Because it is a relatively neutral ground with an immense number of portals where you can be somewhat safe from the gods and Blood War.
Make another place that can do the same and more and voila! You have the next planar uber-city and Sigil eventually becomes a vacant ghost town where a massively powerful Lady of Pain wanders empty streets.
Of course, I never said it would be easy or quick. It'd take lifetimes and probably wouldn't ever see fruition. But if someone could pull it off, you would "defeat" the Lady without ever worrying about being flayed.
Just don't go naming the city "Union". Someone tried that, but Sigil survived.
Make her irrelevant.
Why is Sigil so important? Because it is a relatively neutral ground with an immense number of portals where you can be somewhat safe from the gods and Blood War.
Make another place that can do the same and more and voila! You have the next planar uber-city and Sigil eventually becomes a vacant ghost town where a massively powerful Lady of Pain wanders empty streets.
Of course, I never said it would be easy or quick. It'd take lifetimes and probably wouldn't ever see fruition. But if someone could pull it off, you would "defeat" the Lady without ever worrying about being flayed.
Just don't go naming the city "Union". Someone tried that, but Sigil survived.