After applying for XAT is their need to separately register for XLRI and deposit its fees separately?

Yes, you need to apply for XLRI separately. The application form of the XAT and XLRI is similar and you need to pay an extra amount for applying for XLRI. XAT exam is conducted on behalf of XAMI. You should register for admission at XLRI just before the last date to avoid any last-minute complications. 

If you are registering only for XAT, you need to pay only 1500 for registration. Whereas, if you are registering also for XLRI, you need to pay 250 rupees extra. 

Also, in the XAT registration if you are applying for XLRI then you are supposed to choose the program of your choice i.e. Business management/ Human resource management/ Global business management and general management program.