Here is the corrected 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]

        # Process 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. **Thread-Safe Access:** All accesses to the shared `jobs` and `results` dictionaries are protected by a `threading.Lock`.
2. **Lock Released During Processing:** The processor function is executed outside the lock to prevent it from blocking other threads, improving concurrency and responsiveness.
3. **Atomic Operations:** Reading job data, writing results, and deleting jobs are protected within critical sections to prevent data races.
4. **Safe Result Retrieval:** `get_result()` also uses the lock to ensure consistent reads from `self.results`.

### Example Usage

```python
import time

def slow_processor(data):
    time.sleep(0.1)
    return data * 2

queue = JobQueue()
queue.add_job("job1", 5)
queue.add_job("job2", 10)

# Process jobs in a thread pool or separate threads
import concurrent.futures

with concurrent.futures.ThreadPoolExecutor() as executor:
    futures = [
        executor.submit(queue.process_job, "job1", slow_processor),
        executor.submit(queue.process_job, "job2", slow_processor)
    ]
    concurrent.futures.wait(futures)

print(queue.get_result("job1"))  # 10
print(queue.get_result("job2"))  # 20
```

This implementation ensures thread safety, avoids race conditions, and maintains efficient concurrency by minimizing lock contention during processing.