Does the word have another meaning than something that has to do with washing? It does not seem to fit at all in the context of this sentence
“Ganhava muito pouco e passava fome, tinha tanta fome que desejava encher o estômago com a lavagem que dava aos porcos.”
“Lavagem” means also “bran” or what is left after grains are crushed.
In this case it’s like “swill” or “slop” in English.
=)
In this case, “lavagem” is a lot of food remainings that people in small rural properties accumulate for giving to the pigs.
Like I said… swill or slop in English. 
Ok, thanks a lot! I thought something like that, because I know the story, but I was a little confused.
I had the same problem when I read this story. I thought it was something along the lines of “feed.” This clarifies all my doubts. Thanks!