I was actually wondering if Karlach is supposed to be a Paladin of Tyr.
Anders, the "Tyrite" in the toll house, was obviously lying. He carries the Sword of Justice. Where did he get it from? Was he really a Tyrite ever?
What if the Sword of Justice was actually Karlach's.
Think of her story. She was a demon slayer in Avernus. However, she originally came from Baldur's Gate because she says she has to return home to Baldur's Gate to make the people who enslaved her in Avernus pay.
If you look at some of the higher levels of the Paladin class, Karlach could have been an Avenging Angel, able to even sprout wings and fly. That would have made her an incredibly powerful demon slayer and also able to fly up to the nautiloid when it showed up and therefore board it. Only because she became infected did she lose all her super high level stats and became like a level whatever noob.
The Sword of Justice would, therefore, be very appropriate if it was her sword and she had been a Paladin of Tyr who had been caught up in the Descent of Elturel and then captured and enslaved by Zariel and forced to slay demons in the hells.
Either way, I don't think you'll help her slaughter a bunch of innocents or anything. My guess is that you're going to help her, as a side quest, wipe out a bunch of cultists who worship the demoness Zariel, who, by the way, is after you already.