The requirement asked by your customer can be fulfilled by configuring kerberos authentication for the application .
Once kerberos is enables, and users tries to access the application and if the resource is protected, the user will be automatically authenticated with his machine userid/password which is authenticated through AD.
But below are pre-requisite before you consider the kerberos authentication :
All the clients machine ( machine through which application is accessed ) is present in one domain under AD ( let say AD domain as : abc.com )
All the clients id's should be under the same AD domain ( abc.com ) and clients are accessing their machine based on AD authentication .
The application which is to be access should also present in the same AD domain ( abc.com )
WLS server which is hosting the application should be present in the same AD domain ( abc.com )
Refer to below link for more details :