I am trying outsmart these tragic systems designed in hell knows when. I managed to nail this last year, but this year Lufthansa seems to killed it. Allow me to explain.
I have to get pretty much all across the world from Lithuania to New Zealand. Last year I managed to book this in one lump via Lufthansa with 1 week layover in Singapore and months later with a week long layover in Tokyo (both legs stopping in Frankfurt).
This year I am trying to replicate something similar but stop in Malaysia, Bangkok or Singapore, but looks like Lufthansa site claims The selected route cannot be booked online or is not served by Lufthansa. Although booking flight straight from Vilnius to Auckland works (but obviously I do not want 33hr long journey with no break).
Booking thru Thai Airways site could almost work, but then they do not even recognise Vilnius as a city. Booking from Air New Zealand does not allow to start your multi-part journey from Europe. Epic fail.
I have tried using these awful, awful world-the-globe pages from both alliances which seem to be broken (would never complete the journey). Sites like Skyscanner or Kayak suggest flying via Russia (lol).
Is there a site that I am missing, perhaps some more advanced alliance search tool? Please help me tackle this problem. I do not want to pay thousands of dollars for what is worth around €1.5k.
Edit: David asked for more information why I think that sites are awful. Well, first of all, none of them allow to search actual multipart flights. One World round the world tool only lets you fly one direction (literally round the world! haha, you get it guys!). Star Alliance doesn't even work without Flash player. In year 2015, trillion dollar business is using web technology that is decade old (the rest looks like its build on IBM's WebSphere, so theres another few hundred million of expenditures).

