To provide a steady rest mechanism of a lock case for a door, which is applicable to an offset door, and especially to a door having a large door thickness, under the circumstances that the offset doors have been widely spread in recent years.

The steady rest mechanism copes with the offset door by matching lengths of right and left steady rest bars with outside and inside door thicknesses, and by changing directions of the respective steady rest bars. Alternatively, the steady rest mechanism flexibly copes with both a non-offset door and the offset door and also flexibly copes with the door having the large door thickness, by adding an extension bar to either the right or left steady rest bar, as needed.