Have you checked with Avaya Technical Support?
Generally, documentation (and competitors) generically refer to Sybase ASE (or Sybase SQL Server) as 'Sybase' or 'Sybase Database'. The product is now SAP ASE.
That aside, Nortel Symposium embedded the ASE database (I was on the fringes of the team that sold the licenses to Nortel and have dealt with Symposium questions/connectivity over the years).
Technically, there is no reason that you cannot use a current ASE client (e.g. 15.7 or 16.0) ODBC driver (from an SAP ASE SDK service pack installation) against the older ASE. The ODBC driver was long ago converted to a Wire Protocol driver, so does not need OpenClient installed underneath it. Current versions are certified on newer OS and hardware combinations and should be able to talk to the older ASE release, even thuogh it was long ago EOL'd. To access the SWDC to obtain the download, you will need to have an S-user ID as a current SAP customer.
License is another discussion, however. The embedded ASE in Symposium was intended for access by Nortel-supplied software only. If you have not done so already, you may have to license the ASE for full-use access to use 3rd-party software against it. Check your license rights with Avaya and your SAP Account Executive.
If you have already licensed the ASE for full-use, then you should have access to the SWDC to get the latest SDK for the connectivity you need..
HTH
Chris