What are some ways for a child to strengthen his lungs back to normal after a bout of pneumonia?

Time, usually. Most forms of pneumonia in children do not produce permanent changes in lung tissues, and with time and gradual increases in physical activity your child should recover uneventfully. If, however, they fail to do so, would strongly recommend they being seen by a pediatrician or pediatric pulmonologist. Truly believe and hope this will not be needed. Hope they get well soon.