If a person had mercer infection in their lungs, should or shouldn't they check the lugs Again to make sure it?

It's not "mercer infection". It's MRSA -- methicillin-resistant Staphylococcus aureus. MRSA. If someone has been treated for an MRSA infection in the respiratory tract, then a post-antibiotic sputum culture should be run to check for effectiveness of treatment.