Just curious, which credit card is this?
And I would assume that DL or AA wouldn't get you into the partner lounges, but I could be wrong. Since you fly UA/LH and *A isn't on the list, I'd go for Lounge Club. Although I've only been to their lounges a few times, I have been satisfied with them.
Besides the credit card offer, I'd go for *A gold. With that, you and a guest get lounge access when flying *A.