Gone are the days we had to position to Saint Petersburg to get a low first class fare from Lufthansa. This week, Lufthansa and Swiss announced a so-called partner sale to many destinations worldwide, for premium economy, business class and first class. The low fares only are available if you travel in pairs. Not all offers have been published, and some can only be booked via an online travel agency.
For instance, it's very hard or even impossible to find the first class fare of 1,890 euro return from Amsterdam to Bangkok on Lufthansa.com or Swiss.com, but it can be found via e.g. momondo.nl. The regular warnings for booking via an OTA apply: always pay with a credit card, even if there's a fee, and avoid all the upsell stuff such as choosing your seats and getting travel insurance. For premium cabins, choosing seats is mostly free of charge with the airline itself and travel insurance is always cheaper when bought directly from an insurance company.
Apart from all the other fares, notable ones are Bangkok in business class for 1,090 euro, Delhi for some 1,650 return (per person) in first class. There is not a single overview of all low fares, but you can find some overviews here, here, and here.