They didn't have to. The immune system is largely inactive in and oblivious to the airspace of the lung. It would only be when the roots breached the walls and entered the blood that the immune system would get wise.
No, you are quite confused. Species of leukocytes often squeeze through capillary walls to exit the bloodstream, wander around in the tissue, and go back. The immune system is very active in the lung, it would be absurd for it to be inactive in a site so exposed to pathogens (frequent inhalation, thin epithelium). In fact, the inflammation-like context is one reason that the lung is a common site for metastatic cancers.
Now "dealing" with the roots, I don't know. Would you expect the macrophages to swallow the roots whole? B-cells producing antibodies to aggregate the plant? Normal plants already survive much harsher environments than mere immune systems, they grow on soil exposed to the elements.