Here's the corrected and thread-safe implementation of the `JobQueue` class that fixes the race condition using proper locking:

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

        with self.lock:
            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)
```

### Key Fixes and Improvements

1. **Added a Lock:** A `threading.Lock()` is used to synchronize access to the shared data structures (`self.jobs` and `self.results`).

2. **Protected Critical Sections:** All reads and writes to shared state are enclosed within `with self.lock:` blocks to ensure atomic operations.

3. **Minimized Lock Holding Time:** The actual processing (`processor(data)`) occurs outside the lock, allowing other threads to access the queue concurrently and improving throughput.

4. **Consistent State Management:** The job is removed from `self.jobs` only after the result is successfully stored in `self.results`, preventing data loss in case of processing errors.

This implementation eliminates the race condition and ensures thread-safe job processing and result retrieval.