Well, you've got readers, and you've got writers, and you need a lock, so.... how about a readers/writer lock?
The reason I mention that up-front is because (a) you might not be aware of it, but more importantly (b) there's no standard RW lock in C++ (EDIT: my mistake, one was added in C++14), so your thinking about this is perhaps being done in the context of std::mutex. Once you've decided to go with a RW lock, you can benefit from other people's thinking about those locks.
In particular, there's a number of different options for prioritizing threads contending over RW locks. With one option, a thread acquiring a write lock waits until all current reader threads drop the lock, but readers who start waiting after the writer don't get the lock until the writer's done with it.
With that strategy, as long as the writer thread releases and reacquires the lock after each transaction, and as long as the writer completes each transaction within your 1 ms target, readers don't starve.
And if your writer can't promise that, then there is zero alternative but to redesign the writer: either doing more processing before acquiring the lock, or splitting a transaction into multiple pieces where it's safe to drop the lock between each.
If, on the other hand, your writer's transactions take much less than 1 ms, then you might consider skipping the release/reacquire between each one if less than 1 ms has elapsed (purely to reduce the processing overhead of doing so).... but I wouldn't advise it. Adding complexity and special cases and (shudder) wall clock time to your implementation is rarely the most practical way to maximize performance, and rapidly increases the risk of bugs. A simple multithreading system is a reliable multithreading system.