There’s a current discussion on Flyertalk of a glitch at Lan.com that allows you to book tickets between the US and Europe without being dinged for a fuel surcharge. That’s a substantial savings; the “YQ” charge usually runs about US$250 roundtrip.
This appears to work best with British Airways, or at least to and from Heathrow or on fitineraries transiting Heathrow. Heathrow seems to be the key here, and and the need for British Airways stems from the difficulty that LAN has in pricing and ticketing multi-carrier itienraries.
It’s worth reading through this post by Flyertalker djohannw who has plenty of experience booking at Lan.com.