Even if you had already moved in, you could not have demanded anything for damages, just withheld part of the rent.
I personally feel they were obliged to warn you about the lift but would that have changed anything? Finding an apartment is extremely difficult and despite the bad timing of the lift, it would have somehow worked out.
Good luck finding another apartment and hopefully it will be even better than the previous one.
It seems very strange the landlord is using a lawyer already unless this is his prefered way of doing business.
The OP is American, probably not used to the ways ofd Switzerland and may have come accross a bit "heavy handed" during the discussion, entitled possible which has resulted in this situation.
Move on, you've lost the appartement either before you move or at the next moving date by termination.
You have no chance of winning, lift was unavoidably delayed by well documented chip shortage due to Covid. We did all that was possible however, unfortuantely this was delayed by a further period beyond our control.
Please don't forget to pay court costs on the way out, large lawyers' bill is in the post
Result Chf 6-7k pissed up against the wall and still no lift of appartement.
Most landlords do. It's not only landlords that can be the nasty one's!