"Lousy" also has a definition of being infested with lice (the singular form of which is louse); according to the Etymology Dictionary this may be the original meaning
(https://www.etymonline.com/word/lousy)
From there, it seems to have developed as an American slang to describe "infestations" of other kinds.
My mom who is not British and has spent almost no time outside of the Great Plains uses this term. I think the “lous” come from louse, the singular form of lice. A great abundance of not a great thing.
TIL! But my partner has heard it used in the UK like "I'm lousy with options" as in, I'm overflowing with choice. That was a fun convo as I was like ... What??