James...
Are you aware of EU Regulation 261. This regulation applies to all airlines flying into or out of the EU or those travelling on EU based airlines, which Lufthansa most certainly is. If your flight was cancelled due to weather, you were entitled not just to a refund but also compensation. Weather has been found to not be "extraordinary circumstances" by the courts who have upheld the rights of passengers to be compensated when flights are cancelled due to weather delays. Although your flight originated in the US, the regulation applies because you were travelling on an EU based airline, travelling to an EU destination. You were entitled to a refund plus €600 compensation.
Now you are faced with the dilemma that you voluntarily accepted a lower offer. However, the law is still on your side. Lufthansa were legally obligated to make you aware of your rights under the Regulation. It is clear from your post that they did not do so. I would write to Lufthansa and tell them you have only just become aware of your rights under this law. State that they were in breach of this law by failing to notify you of your rights and that you would not have accepted their offer had you been aware of them. Ask them to reinstate your rights on this basis. If they refuse file a complaint with
Luftfahrt-Bundesamt (LBA)
DE - 38144 Braunschweig
You can call them on +49 531 23 55 115 (9am to 4pm Mon to Fri German Time)
You can email them on
fluggastrechte@lba.de
The website is :
http://www.lba.de
The airlines are working hard to limit your rights as a passenger and are taking an increasingly hard line trying to avoid paying you the compensation you are legally entitled to. They may try the extraordinary circumstances excuse, but they cannot get out of their failure to advise you of your rights. You were entitled to know these and would not have accepted their offer had you known them. It is on this basis you should fight to overturn their decision.
I hope that helps and good luck.
Jim