Do you still have your boarding pass? if so, you can fax or mail it to US along with a few details about the flight, and you will get your credit (and usually pretty quickly). There is a Request Missing Miles link in your US account which has all the details, address, etc.

If you do not have your boarding pass, I'd email/call US. If you have a preferred status, use your preferred desk. Advise them that you do not have the BP but provide whatever details you do have, and ask them what documentation you can provide. If you are clear about the challenges you are facing (i.e. no longer have BP and LH wants $20 to help) they usually will work with you. You may initially be told "the boarding pass is the only way we will do this" because that seems to be in their script but I've had good experiences with US in the past, trying to get partner miles without the BP.

If you used a mobile BP for LH then that is actually to your advantage as US does not right now have any policy on how to handle retro partner mileage requests when there's no paper BP to send over. So they are very flexible here.

Two details that can help significantly: the ticket number, which is often found on the credit card statement, and your seat assignment.