For example: “According to Chinese tradition, the saw was invented by Lu Ban.”
Is there a name for when two consecutive words are ‘mirrors’ of one another? Also, can you think of any other commonly occurring examples?
I’d probably call it something like a palindromic word pair.
“Palindromic word pair” (or something of the like) does seem to be the going descriptor. I was actually pondering something like “reversophones”. Thanks.
The most awesome collection of palindromes ever, set to music - Weird Al’s song, “Bob.” 
The president of Palindrome Society was given a brand new car for his 25th year with the Society.
A Toyota