Lavabit's situation was different because they were a "choose not to look" solution, not a "can't look" solution.
That said, Signal is centralized, so it's not like they are particularly robust against that sort of thing, just that other than getting Signal shut down, any strong-arm tactics are unlikely to result in very useful information from OWS.
https://www.aclu.org/blog/free-future/new-documents-reveal-g...
Doesn't matter how you design the architecture. Someone can just force them to "update" their app via the app store, and all of your privacy is gone.
https://github.com/WhisperSystems/Signal-Android/blob/master...
I honestly don't see a revolution coming if Signal is shut down. There will be some angry folks, sure, and that will last a while, but then everyone will move on. Exactly as it happened with the Snowden revelations.
If Signal goes down I would speculate a lot of people who already have things like encrypted messengers, adblockers, things of that nature, would start to move to the only-vpn, no javascript run ever, no Google Play Services on your phone, no proprietary software at any stage of your life sort of deal.