locking $0 has no difference from locking a "separate" file

Quite true, but my words were "creating a separate file" :-)

Also, I was reading between the lines and (possibly incorrectly) came to the conclusion that the OP was trying to prevent simultaneous access to a script. If that was the goal but there were multiple copies of the script or mutliple names (links) then no, the $0 approach wouldn't work.