Hi Duncan, sorry for the delayed response!
Our team here (at Intel) is definitely interested in keeping the LLDB Linux builds green, and we can commit to watching the bots and contacting anyone who doesn't fix a build-breaking commit.
During the Hacker-Lab and LLDB-BOF last week, it sounded like many people are interested in running LLDB in all sorts of scenarios, and getting continuous build/test runs on additional platforms can only help the project get more stable.
I'd be glad to assist you in getting the initial builds passing. Currently I'm using libstdc++ and my colleague Matt Kopec (cc'd) has LLDB building with libc++ (both of us build with ToT clang on Ubuntu). If you're still interested in doing the work to set up the bots, we can discuss what configurations are reasonable/most beneficial to run.
Cheers,
Dan