To make it simple suppose I had a note from Lou Gehrig when he was a kid that says, "Thanks for the Christmas gifts" in Lou's handwriting. Furthermore, instead of signing it Lou Gehrig he just writes Lou. Now the fact that he didn't write Gehrig, does this now technically not make it a signature or autograph? Furthermore, being the fact that it is a note does this take away from it being an autograph? Since it was written as a teenager it would probably be the earliest Lou Gehrig signature in existence, I guess if you would call it an autograph.
For simple argument sake there is strong provenance that supports that it was indeed Lou Gehrig who wrote the note, so lets not argue whether it is legit or not, but instead focus on the fact Gehrig is not after Lou and the fact that it is a note and not some fan asking for an autograph. Obviously, one way or another its valuable, but once again I wonder how the market would see it?