I don't know how universal legal principles are. I don't know what law would apply when you use a German carrier to fly from the US to Italy. But I do know that German contract law is the same as contract law here in the UK, and it works on the principle of "offer - acceptance - consideration". If you have made an offer to buy something at a certain price, and that offer is accepted, then there is a valid contract. LH quoted you a fare, AND they took your money... that's a valid contract, at least under German law.
They probably realised they'd made a mistake when they tried to issue your tickets and "the system" wouldn't let them. "The system" can be overridden (I used to work for an airline) - but in order for this to happen someone will need to own up to the mistake they made, and get someone higher up in the company to do the manual override. They are trying to bully you into backing down from the contract so that they don't have to own up to their mistake.
If I were you I'd fight. Don't talk to the reservations department - go straight to customer relations, and make sure you talk to someone high up.
Good luck!
(Edited for typos)
[This message has been edited by Aviatrix (edited 10-21-2003).]