Answer
The Web Express IDE does not allow for integration of custom context menu items like 'Add ArcGIS Identity'. Another limitation with Web Express is that the ArcGIS Server installation cannot automatically integrate the ArcGIS Server controls into the Toolbox.
The ESRI Developer Network topic in the Related Information section outlines how to manually add an identity to the web.config of an application. This procedure should be used with Web Express or when it is necessary to deploy an application to a Web server that does not have Visual Studio installed.