Are there home remedies that can treat a viral lung infection?

No. Viral infections are not treated with antibiotics, most resolve with standard care of fluids , fever control. Serious infections require hospitalization, steroids oxygen and sometimes mechanical ventilation.
Yes, rest and time. Viral infections are almost always self-limited, and "home remedies" are usually all that is needed, as long as you don't require hospitalization. The other home remedy to keep handy is your phone, in case you get sicker, and need medical attention, you can call your doctor. Keep hydrated, take Acetaminophen or Ibuprofen to help make yourself comfortable, and curl up with a good book.