The lift from the old Tube Ticket Hall to the Northern line is now
open at King's Cross. It travels from level "-1" to level "-3", and
only has these options. But when the lift gets about half way between
them, or perhaps nearer to "-3", there is a tunnel on the west side
(that's the side you enter the lift on at level "-1" and the opposite
side to the exit at level "-3").

The tunnel is all lined properly like other public areas of the
station. It curves to the right (the north).

Where does it go, what is it for, and why is it lined line a public
area?