If LH says the flights have been credit to LH M&M, you are hosed until you are able to get LH to change that response. Especially if the tickets were purchased from LH.

Ask LH what account it was credited to?
And how it was creditted to LH if you have no account.

LH has to approve the crediting of the flights to UA -- not an unilateral UA decision (except in very rare cases).

To you base questions, this very uncommon. This is not going to be an easy, fast resolution and if UA is will to go to bat for you, give them anything they ask for.