I am applying to be a lecturer, where most of my references are professional references. I am being asked for a mailing address for references. Professionally, it seems awkward to ask for someone's mailing address. I understand this is easy in academia, as one can put down the department address. Similarly, I can put work addresses for professional references. However, a few references have since retired. What can I do in this situation?
Many retired academics keep their university email address. Try that. If you can't find an address, ask their old department if they can give you updated contact information. This might include physical mail addresses.
Many retired academics still have a web presence and a web search may turn them up.
But you shouldn't be listing references that you haven't already contacted, so you should have some means of asking them what to do. They will supply an address if they choose to.