Because of the narrow stiles and rails of steel doors, the lock box typically cuts into the glass. The notch in the glass is large enough for the body of the lock box. Then the sub-escutcheon and escutcheon cover the lock box and transition into the glass.
When designing the doors for a project there are a number of options of how this projection is treated. When the door has a single large pane of insulated glass, the choice is really just the size of the overall escutcheon cover relative to the scale of the door. When the door has divided lites, then the choice becomes the relationship of the escutcheon to the breakups in the glass. The balance in the use of escutcheons, TDL's and their relation to lever heights becomes the design challenge. In many projects the lite pattern, and thus the escutcheon and lever locations, become the driver for horizontal alignment of all the windows and doors throughout the entire project.
The other challenge we face with today's steel doors is the use of the insulated glass. By design the insulated glass has a colored spacer bar between the two lites of glass and this glass edge needs to be hidden whenever possible. Tucking the lock box below a TDL will always help hide the appearance of the corner of the insulated glass. Planning the lock box height and relation to TDL's in the initial design is recommended.