The race condition occurs because multiple threads can access the shared dictionaries (`self.jobs` and `self.results`) simultaneously without synchronization. Specifically:
1.  **Double Processing:** Two threads can check `if job_id not in self.jobs` at the same time, both see the job exists, and both proceed to process it.
2.  **Data Corruption:** Multiple threads writing to `self.results` or deleting from `self.jobs` concurrently can cause data loss or `KeyError` exceptions.

To fix this, we need to use a `threading.Lock` to ensure that access to the shared state is atomic. We should also optimize the locking to allow concurrency (processing jobs in parallel) by releasing the lock while the actual work (`processor`) is being done.

Here is the complete fixed implementation:

```python
import threading

class JobQueue:
    def __init__(self):
        self.jobs = {}
        self.results = {}
        # Initialize a lock to synchronize access to shared data structures
        self.lock = threading.Lock()

    def add_job(self, job_id, data):
        # Protect the shared 'jobs' dictionary
        with self.lock:
            self.jobs[job_id] = data
        return job_id

    def process_job(self, job_id, processor):
        # Phase 1: Claim the job
        # We must acquire the lock to safely check for the job's existence
        # and retrieve it.
        with self.lock:
            if job_id not in self.jobs:
                return False
            
            # Atomically retrieve the data and remove the job from the queue.
            # Removing it here (claiming it) prevents other threads from 
            # picking up the same job while this thread processes it.
            data = self.jobs.pop(job_id)

        # Phase 2: Process the job
        # We release the lock here to allow other threads to add jobs or 
        # process other jobs concurrently.
        try:
            result = processor(data)
        except Exception:
            # If processing fails, we return False. 
            # Note: The job has already been removed from the queue.
            return False

        # Phase 3: Store the result
        # Re-acquire the lock to safely write to the results dictionary.
        with self.lock:
            self.results[job_id] = result
        
        return True

    def get_result(self, job_id):
        # Protect the shared 'results' dictionary
        with self.lock:
            return self.results.get(job_id)
```

### Key Changes Explained:
1.  **`self.lock = threading.Lock()`**: Added a mutex lock in the constructor.
2.  **`add_job`**: Wrapped the dictionary write in `with self.lock:` to prevent race conditions when adding jobs.
3.  **`process_job`**:
    *   **Atomic Claiming**: The check `if job_id not in self.jobs` and the retrieval `self.jobs.pop(job_id)` are done inside the lock. `pop` is used to read and delete the job in one atomic step. This ensures only one thread can process a specific job ID.
    *   **Concurrency**: The lock is released *before* calling `processor(data)`. This allows multiple jobs to be processed in parallel by different threads, which is the main purpose of a job queue.
    *   **Safe Write**: The lock is re-acquired before writing to `self.results`.
4.  **`get_result`**: Wrapped the dictionary read in `with self.lock:` to ensure thread-safe retrieval.