Only Cisco MPP phones will work with a 3rd party server. If you have a Cisco Enterprise Phone (which works per default only with CUCM), you need to convert it first to an MPP phone. How to verify, if you have an Enterprise or MPP phone and the conversion has been discussed here many many times.
And honestly: Why don't you ask this question in the Avaya forum? They have to tell which 3-party phones the support and which specifications the phones must have, and how to configure it.