Here is the fixed implementation of the `JobQueue` class with proper thread synchronization 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
            # Atomically claim the job
            data = self.jobs[job_id]
            del self.jobs[job_id]

        # Process outside the lock to avoid blocking other threads
        result = processor(data)

        with self.lock:
            self.results[job_id] = result

        return True

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

### Explanation of the Fix

The original code had a race condition where multiple threads could simultaneously read and write to shared state (`self.jobs` and `self.results`), leading to inconsistent behavior or lost updates. The fix introduces a `threading.Lock()` to ensure thread-safe access:

1. **Atomic Job Claiming**: The job is checked and removed from `self.jobs` within a single locked block. This prevents multiple threads from processing the same job.
2. **External Processing**: The actual job processing happens outside the lock to avoid blocking other threads from accessing the queue.
3. **Safe Result Storage**: The result is stored within a locked block to ensure thread-safe writes to `self.results`.
4. **Consistent Reads**: The `get_result` method also uses the lock to safely read from `self.results`.

This design maintains both correctness and performance by minimizing lock contention while ensuring all shared state modifications are synchronized.