Here's the complete fixed implementation of the `JobQueue` class with proper locking to eliminate the race condition:

```python
import threading

class JobQueue:
    def __init__(self):
        self.jobs = {}
        self.results = {}
        self.lock = threading.Lock()

    def add_job(self, job_id, data):
        with self.lock:
            self.jobs[job_id] = data
            return job_id

    def process_job(self, job_id, processor):
        with self.lock:
            if job_id not in self.jobs:
                return False

            data = self.jobs[job_id]
            result = processor(data)

            self.results[job_id] = result
            del self.jobs[job_id]
            return True

    def get_result(self, job_id):
        with self.lock:
            return self.results.get(job_id)
```

**Explanation of the Fix:**

- A single `threading.Lock()` is used to synchronize access to all shared data structures (`self.jobs` and `self.results`).
- The `with self.lock:` context manager ensures that the lock is acquired before accessing shared state and released afterward, even if an exception occurs.
- All read and write operations on the shared dictionaries are protected within the critical sections.
- This ensures atomicity for each operation and prevents race conditions when multiple threads interact with the queue concurrently.

This implementation is now thread-safe and maintains data consistency under concurrent access.