Scheduling a response callback
Disclaimer: I don't know Android. I've wrote two or three programs for it. 

Also, I don't have your full code so can't be sure about some of the classes this code relies on.


Test name has an "and", seems like two tests?
Test throws Exception, do you have tests for that?
You don't need to start test name with tests, unless you use JUnit 3.
When LooperThread runs, it calls Looper.prepare() and Looper.loop(). What these do?
LooperThread extends Thread, why not implement Runnable? You only implement run() then?
Further reinforcement to point 1) - you have more than one assertion. If verify buckles, other assertions aren't tested. Is that fine?
Why do you need a final boolean[] threadBlocked = {true}; over just a final boolean? I found no other reference than to that one element, via threadBlocked[0]?
Is this test alone it it's class? If so, I'd extract mocking out of it. Readability / clarity / easier to spot things.
Have you tried structuring the test into classic given - when - then or assess - act - assert?