Glenn and Topgun are correct: when the top lever is brought over to its widest position to the right, the safety slide retreats to a rear 3rd position which is safety off. It will only stay there if the screw you have asked about is screwed in about one turn. The gun is now a no safety live bird gun (or in my hands a target gun). Turn the screw out and you have an automatic safety hunting gun once again.
Many of these selective Lefever safeties have been disabled or are broken, probably due to lack of understanding. My local gunsmith has been able to restore them for me on 3 Lefevers. The mechanism is well described in the reproduction Lefever catalogs available thru Cornell (http://www.cornellpubs.com/old-guns/historic-lefever-firearms.php).
Another upstate New York gun company, L.C. Smith copied this concept with their 3 way safety. Conceptually, it works the same but functionally it is dangerous because one can mistakenly pull the safety back into the fire all the time position and not realize it.