@lovetheview Here’s a suggestion: get a suitably qualified telecommunications technician (which includes most electricians) to check the connection on-site. You’re likely to have a main telco box somewhere where the incoming lines terminate. There will then be one or more cables going to a termination box somewhere near the lift. In this box there should be a connection between the line and the physical phone in the lift. It’s likely this is the link that’s missing.
A tech will be able to, at a minimum, confirm where the line gets to and where it stops. They may be able to reinstate the connection.
If it can’t be reinstated, I would get a written report from the tech and forward it to the lift company with a very specific order to complete the connection, noting that if they fail to do so they will be in breach of their contract with you to maintain the lift and, no doubt, in breach of legal requirements. Maybe get a lawyer to draft it for you.
Good luck!