Today lightning started to hang up thunderbird shortly after startup with 100% cpu, no I/O and constant memory usage. I verified the cause by deactivating it. Since this also happens with a completely different installation and a different server-side account, I suspect the server (owncloud) sends something awkward. I read about debugging a thunderbird extensions using the firefox tools, but I cannot connect the debugger, since the main drawing thread is blocked (and thus the connection cannot be accepted). The error console seems to be empty.
Is there any other known strategy to debug a running thunderbird/lightning app? Can I dump the js state? Log all lightning actions to the console? Any other idea to pinpoint the culprit?
You can use the remote debugging capabilities to capture a profile. This should be working even if most things are hanging, but from what you wrote it seems you've tried. If the problem is that you cannot access the dialog that asks to accept the connection, you can set a few devtools prefs to auto-accept connections. I believe this is devtools.debugger.prompt-connection which needs to be set to false.
Regarding logging, you can enable calendar.debug.log and calendar.debug.log.verbose in the advanced config editor. You can then set XRE_CONSOLE_LOG to output the console to a file. There is a page (although not official, or at least outdated) on debugging xulrunner apps. This pretty much applies to Thunderbird too.
You may also be lucky in contacting the Lightning maintainer to discuss debugging this, he is available on irc.mozilla.org #calendar and is named Fallen.