You cannot see LUD if you just check online the status.
You should sign up to an account (as customer I guess) on the INS website
https://egov.immigration.gov/cris/jsps/index.jsp
go to login and register. Then you can introduce your cases and create a portfolio and set up e-mail so when the message will change they will e-mail you.
You will see there also LUD as a date. If LUD will change but message will be same - they will NOT send you e-mail, so you have to check online your portfolio (not just case status check online) to find out.
Hope this helps!