You have discovered the dangling participle: a participle that modifies a noun that isn't there (or a different noun than the one intended). It is poor English, and you are right to call it out as an error.
Here is one way to correct it:
However, lacking accounts by conquered people about their interactions with the Incas, we cannot know how much of the information of the Inca conquest as related by the ruling class is factual.
The participle lacking modifies the noun we.
(I would also remove the word "as", but that's a different problem.)
Another way to correct it is to put lacking into a subordinate clause with its own subject and linking verb, like this:
However, since accounts by conquered people about their interactions with the Incas are lacking, it is unknown how much of the information of the Inca conquest as related by the ruling class is factual.
And there are many more ways to correct it, of course, including rewording from scratch:
All the information we have about the Inca conquest comes from the Incas, not from the peoples they conquered. We can only guess what the Incas omitted or distorted.
I can't tell if this represents the intended meaning of the original sentence, but this is clear, straightforward, grammatical English.
As dangling participles go, the one you found is not so bad. A reader could perhaps understand the lacking clause as a huge adverb that modifies is unknown. Perhaps one could regard the lacking clause as a sort of absolute construction. But those interpretations are stretches that a writer should not ask a reader to perform. The original sentence is clumsy and, as you observed, illogical, even if the meaning is passably clear. It's a mistake, the result either of carelessness or pretentiousness. People do it, though, even educated people, so if you read enough English, you'll need to learn to trudge through it and extract the intended meaning.