Nothing wrong running a lift phone behind a PABX. Just about every building we put in a system that has a lift gets an extension for the lift over a stand alone line.
Of all the ones I have done they are simply hotlined to the lift company's call center. Dial-up data isn't involved.
You mention the current system failing. I would suggest it would be a 99.9% probability that the PABX failed rather than ISDN. ISDN is rock solid.
My overall suggestion would be buy them a Cisco SPA112, hook it up to WxC's managed VFX service and job done. Completely stand alone. Connected to the the best PSTN replacement available and you don't have to worry about settings on the ATA as WxC will auto-provision. If you are confident with your ability to set up an ATA then 2Talk might be the go but it will be up to you to support rather than the provider.