I needed to call Lufthansa, and they don’t make it very easy to get their phone number. A couple screens in on Lufthansa’s USA site, you’ll get the (800) 645-3880 phone number.
Here’s the interesting bit: I called that number and got through to your typical “press 1 if you would like to hold for 5 minutes”, “press 2 if you would like to hold for 7 minutes” sort of menu. While I was holding for reservations, I remembered calling a different number ending in LUFT previously, not getting any kind of menu and not waiting at all for an agent.
The number is 800-399-LUFT and it took me straight to reservations and a person answered right away. I had somehow tracked this number down via the main Lufthansa site, even though Lufthansa USA would prefer that you wait several minutes before they talk to you.