Lucent/Avaya PBXs have a number of phone types.
Some are very proprietary. A few (vey few) are ISDN. Some are simple analog. The old digital phones (6400, 7400, and 8400 serise phones) are proprietary connections that only work with other Lucent/Avaya devices. There are others, (like the hybrid series phones) but the 64xx, 74xx, and 84xx are the most common. ISDN phones really didn’t catch on with Lucent/Avaya.
Lucent/Avaya PBXs will almost certainly not be able to make your Asterisk phone ring at the same time as your PBX desk phone. Lucent/Avaya PBXs use bridged appearances to make a phones ring simutaneously in multiple locations.
It is highly unlikely that you’ll easily get your PBX to to recognize an Asterisk channel as a bridged appearance of your phone.
I can think of only one way to do this. You would use an analog station port that would be configured as the bridged appearance of a digital station button. That ZAP channel would be programmed to extend the call to your VOIP phone when it rings.
However, this solution would limit your incoming calls at the Asterisk box to a single call. Even if your PBX phone has three line appearances, there would be no way to extend the second or third incoming call to your Asterisk phone. (Unless you setup three analog lines from the PBX to the Asterisk box.)
There are other limitations to my solution:
You would not get message waiting indications.
Transfer would not work except to another phone on the Asterisk gateway.
Display information would be lost.
Conferencing would have to be done on the Asterisk system instead of using the Conference button as you normally would.
If you want to extend a Lucent/Avaya phone, there are solutions out there that are more tightly integrated, though they typically involve modem-like devices and continuous phone calls to connect the local and remote dvice together. (These are not always cost effective.)