A lot of things were done in h the past despite people not knowing why. The because should be read as a retrospective reason. The originators of the practice at have just found it dealt with odor and so they did it, in retrospect we can add the actual reason it helped.
I don't see a problem with the author using a more modern terminology for "cause" than would have existed at the time, to describe what anyone working with lime plasters appreciates on a basic level; the stuff stays exceptionally white and clean.
Personally I don't like their saying just that it kills off bacteria. It's an antimicrobial/fungicide in general because of its elevated Ph.
I'd prefer the article take the opportunity to educate me about the practical value of lime plaster than restrict itself to the limited education of medeivil minds.
You might not see the problem, but it's factually inaccurate because there is an attribution error.
Oddly in this case where the author could have made a correct attribution he used the word "which" which does not ascribe a cause. If he had simply switched "which" and "because" we probably wouldn't be having this conversation, because the sentence wouldn't have been false. It makes me wonder if the author swapped around the rest of the sentence after writing it originally.
I don't think anyone is suggesting reducing the information content. Even wanting more is just fine and dandy, but the proper way to do that would be to correctly attribute the reasoning of the time, and then add something along the lines of "which we know today does $x."
The sentence is mangled and syntactically incorrect anyway - there's no other reason before the "and". Maybe it originally said "and kills off bacteria" before a "because" was added during the editing process.
But that reason is stuck in a descriptive clause modifying "lime-plaster" or "a coating of lime-plaster".
You wouldn't write "Walls were sometimes whitewashed with a coating of lime-plaster which was white and because lime kills off bacteria." The longer sentence makes it less jarring until you try to parse it carefully, but still very poor style.
I don't think I'm being some kind of prescripivist grammar Nazi here: the rest of the piece is written reasonably professionally and I'm sure the editors would fix that if they spotted it.
Perhaps there was some mediaeval theory relating lime and pestilence?