Besides the nice offer to help from Michelle; did you check out LH's website, yet? I found it relatively easy to find the specific adresses on the website. I am talking about the German branche though (and US, but that one wasn't for a complaint but for a kuddos), don't know in which country you'ld want to file a complaint.

I wouldn't just file a complaint online, though. I would follow up through normal snailmail, at least. Most importantly of all because somehow I've got the idea that going through snailmail makes it easier to get to the right person/department and makes a little more impression. (writing a letter takes more effort than filling out a form and sending an email). Also maybe it's just me (hopefully ), but I found a lack of any response to expressing a particular complaint through email and over the phone whereas filing the same complaint on paper did get response. Can't say anything about the outcome, as we're still in the progress of working on it, but at least getting response is step 1.

Good luck.