Previously I\'ve written some very simple multithreaded code, and I\'ve always been aware that at any time there could be a context switch right in the middle of what I\'m doing
Don't use volatile. It has virtually nothing to do with thread-safety. See here for the low-down.
The assignment to BOOL doesn't need any synchronisation primitives. It'll work fine without any special effort on your part.
If you want to set the variable and then make sure that another thread sees the new value, you need to establish some kind of communication between the two threads. Just locking immediately before assigning achieves nothing because the other thread might have come and gone before you acquired the lock.
One final word of caution: threading is extremely hard to get right. The most experienced programmers tend to be the least comfortable with using threads, which should set alarm bells ringing for anyone who is inexperienced with their use. I strongly suggest you use some higher-level primitives to implement concurrency in your app. Passing immutable data structures via synchronised queues is one approach that substantially reduces the danger.