Interesting fare that just came up – courtesy of exbir.de… Fly from Luxembourg to New York for just $449.
This fare shows on ITA Matrix – the best dates I could find were in late August for $449.
The fare is bookable when searching on wego.com for the dates.
The segments are operated by Luxair and US Airways/American Airlines.
It does work in reverse but the price increases to $663 unfortunately – which isn't a great deal but decent for late summer fares.