This is all a bit confusing because of the multiple uses of the word lobby.
The list posted by Steve above seems to be the lobby correspondents, who are the ones allowed into the press gallery and Members' Lobby. It's also truncated when I view it on my phone - Jon Snow is on the PDF version
I don't think you need to be on that list to broadcast from Central Lobby though - Krishnan Guru-Murthy presents from there fairly often and doesn't appear. There are some details about that here
- that page appears to have been published in response to this incident
. C4 would appear to stretch the rules slightly by anchoring 'other news' bits of their programme from there sometimes.
Steve in Pudsey gave kudos