What is the context for this? Is it from a novel for instance?
To me it is natural, as the speech marks " " are emphasising the information. It does make Mr. Lee sound more important or significant to the reader.
If you change where you put the speech marks, then you change how the sentence is read.
The letter was signed Mr. Lee in "red" ink.
This could mean that though it appears red, it might be signed in blood (as blood is red).