In IMSLP, "Der Leiermann" is in A minor.
But this performance is transposed to G minor.
Are my key identifications correct, and if so, why would Dietrich Fischer-Dieskau and Alfred Brendel (the pianist) lower the key?
The song was published in a key for a tenor, and Dietrich Fischer-Dieskau is a baritone. So he asked the pianist to change it to a key that worked better with his voice.
Most art songs were in fact published in two editions, in different keys: one for soprano or tenor, and the same music in a lower key for alto or bass.
But any time any singer selects a song to perform or record, the singer can and should change the key to whatever works best for his or her voice. It has always been that way, in virtually all styles of music, everywhere in history.
It is only in the last 100 years, in the age of recorded music, that audiences have become accustomed to hearing a song in a certain key, usually based on what they hear in a hit recording.