If I want to implement AD LDS for a single application, does it require Physical hardware or it can be installed/enabled on web server or application server. As usually the web and app servers are placed in DMZ if the above option is not feasible can we put standalone AD LDS server n DMZ.
This technet article should answer most of your questions: http://technet.microsoft.com/en-us/library/cc755080%28WS.10%29.aspx
LDS is suitable for applications that will benefit from storing data in a directory, but as the article states, it's limited as follows:
To the original question: Yes, it can be installed on the same server as your application.