Are there home remedies that can treat a pseudomonas aeruginosa lung infection?

No. No there are none, if you have pseudomonal infection you need special antibiotic, and than longer you wait the worse it will get.
Not really. Pseudomonas is a very dangerous bacteria that infects those who are chronically or critically ill . ( such patients with cystic fibrosis or in the intensive care unit ) it is a it needs to be treated with antibiotics that are active against this germ and that often must be given iv. Sometimes when prolonged therapy is needed it can be completed at home, under medical supervision.