Here's the corrected and thread-safe implementation of the `JobQueue` class, with proper locking mechanisms 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]
            del self.jobs[job_id]  # Atomically remove the job

        # Process the job 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)
```

### Key Improvements:

1. **Thread-Safe Access:** A `threading.Lock` ensures that all accesses to shared state (`self.jobs` and `self.results`) are serialized.
2. **Atomic Job Removal:** The job is removed from `self.jobs` inside the lock to prevent other threads from accessing or re-adding it while processing.
3. **Non-Blocking Processing:** The actual job processing (`processor(data)`) occurs outside the lock, avoiding unnecessary contention and improving throughput.
4. **Safe Result Storage:** The result is stored under lock, ensuring consistency and preventing concurrent writes.
5. **Consistent Get Result:** The `get_result` method also uses the lock to safely read from `self.results`.

This design ensures data integrity across threads while maintaining good concurrency performance by minimizing lock hold times.