If you are referring to the red handle seen above the vault during post-war, it is attached to the only visible controls that could operate the lift leading down into the vault. Also, you would not place such controls out of reach due to the nature of the vault itself. The controls to operate the lift would therefore be within easy reach of the lift area, to allow fast access in the event of an imminent nuclear strike.
I would imagine that there would be an audible warning sound and a delay of several seconds before the lift actually begins to move downwards. The reason I say this is due to the blast doors we see opening as we emerge from the vault in the E3 demo. Once these doors have sealed shut upon first accessing the vault, nobody is getting out for a good while. And so anyone left topside will not be getting into vault 111.
As for your suggestion of a rear vault door, it would not make sense having another way in or out above the vault. The fail-safe that I have suggested earlier in this thread would have been put in place to allow for any blockage (such as an aeroplane falling out of the sky following EMP blast) preventing access to surface level via the topside lift area. This fail-safe would consist of a compression chamber beneath the main vault level (at the base of the vault) that would lead out into a subterranean tunnel.
Anyone still inside the vault could then escape at a later time via the tunnel and emerge into a nearby waterway (most likely https://www.google.co.uk/maps/place/Great+Meadows+National+Wildlife+Refuge/@42.4756627,-71.3330381,2397m/data=http://forums.bethsoft.com/topic/1523172-is-vault-111-built-like-a-submarine/!3m1!1e3!4m2!3m1!1s0x0000000000000000:0xbf6cbd4a2b47e5a4 one). Note that a submersible, such as the one seen in concept art, would be placed at the entrance to the tunnel to provide a means of escape.