Another interesting experience here trying to change an ANCXX fare (basically the lowest and most restrictive fare family in first class). I called in to the 365 number listed above from Skype to request a voluntary change last week, and an agent picked up after literally 1 second after I hit option 3 for English. Now the change I wanted to make was blowing the booking out of the water entirely (dates, origin, destination) and complicated in that it had non codeshare non LH group metal on it but was still something I could piece together using the multi city tool on the LX website. So after feeding the agent dates and flight numbers, he told me the automated system couldn't handle it, he'd have to get a manual calculation for any fare difference and would call me back that afternoon.

I didn't get a call back that day so called in again the next day to get an update - I knew the agent had done something though as I could see both sets of flights under my reservation on the website. I had to wait about 10 minutes on hold this time, before an agent picked up which seemed like she was at the general reservations line as they said there weren't any notes in the booking, and after looking further she said that she'd get someone from the HON desk to call me back ASAP (I'm not HON...), so it appears that this line may ring over to the general call center after a certain waiting period. Well, lo and behold I had a callback from the same agent that had initially taken my call the first time around within about another 5-10 minutes on my mobile, who apologized profusely for not returning my call, and astoundingly the fare difference he gave me was very close to what I'd calculated my own - within about 50 EUR or so from my own calculation, not the thousands I was dreading hearing *especially* because I forced a routing via LAX which has been fairly difficult to get for some time in A even for a new booking.

So, in sum, trying to do these changes is completely YMMV!