Pulmonarias are more or less evergreen through winter in my climate but I do cut them back if they start looking tattered or ratty and certainly before spring.

They are also known for developing powdery mildew after flowering. If you cut them back hard at that point, they will regrow fresh foliage that should stay clean for the rest of the season.

Great

I gave up growing pulmonaria a very long time ago because they were always plagued with powdery mildew without fail. Now, these were older varieties (e.g. Mrs. Moon), so maybe newer cultivars are more resistant -- that I don't know.