I agree with international_man, there doesn’t seem to be much speciality around that I have seen other than Air Crew, Diplomatic, and APEC queues. And I can personally attest that APEC is awesome when arriving in Hong Kong
There may be a few lesser known ways to get expedited entry depending on where you are headed. Take Hong Kong for example, they have a Frequent Visitor e-Channel program where you can get through quickly if you’re a member of certain airline programs with some status… Cathay Pacific Marco Polo Club members qualify, and probably relevant to OP is Lufthansa (not sure what their mileage program is). Tough thing is you need to sign up when you arrive the first time, and then use the e-Channel on future visits.
Another example for Thailand would be the Thai Elite visa. If you’ve got the money (500K baht) there’s expedited service on arrival and departure, limo service, and a 5 year visa included. If I ever decide to spend a lot of time in Thailand (as well as coming and going), I may give this a shot myself!