I am a litigator but do not specialize in travel law. Without knowing the particulars it is hard to say what your best course of action is and how likely it is you could recover against a foreign corporation here in the US. Lufthansa does have officer here though do they not?

This issue as I see it is that you don't have a contract or agreement with Lufthansa. What exactly do you have in writing regarding the situation.

Did you rely in any way on Lufthansa's offer in making travel decisions? What did Lufthansa receive in exchange for honoring these miles?

It certainly is possible to obtain attorney's fees in such an action depending on where it is filed. Many states have unfair business practices acts that provide attorney's fees and treble damages. Other potential causes of action would be fraud and breach of contract.

I am just unclear as to what you have an writing and what assurances were made to you. I recommend you don't provide too many details on a public forum however, as it could come back to haunt you.