You should have posted this in the Swiss/LH Group forum for better/more accurate and faster replied.

Yes, assuming that your itinerary qualify, e.g. BKK-ZRH whereas BKK-ZRK-USA or UK will not qualify, you should be eligible for comp. for cancellation, EUR 600 from LX. It doesn't matter that you ended up cancelling the ticket. LM has nothing to do with this. Whether you will be able to make Swiss pay the comp. is an entirely different Q; Swiss is notorious for playing difficult when it comes to EU Reg. 261/04. Good luck!

You should have insisted that LX rebooked the ticket rather than calling LM to get rebooked. It was clearly the responsibility of LX to rebook you in IRROPS situations like this despite you being on an award ticket. But the reply "contact the issuer of the ticket" is very common/normal in situations like this/as soon as the agent realise that the ticket is an award ticket issued by others, as agents are very reluctant/do not know how to deal with award tickets. And often it works; you are a good example of this.