Frankly, that sounds like someone with zero etymological knowledge made it up because it sounded good. It has absolutely no basis in truth.
The imperative förlåt comes from the verb förlåta, which comes from för + låta. The literal meaning is "for-let" - that is, to leave something behind. And English actually has a mostly archaic word "forlet" which means to forsake or abandon something, for instance in the context of sinning.
Yeah, i went back to check that particular expression and - for lord - ended up being a useless mnemonic created by a novice user, not an inaccuracy on the part of memrise's staff. I also recalled the movie - låt den ratte komma i - and figured - att förlåta - is made up of for and let, which is quite similar to forgive itself.