This is a classic example of a race condition involving shared mutable data structures (`self.jobs` and `self.results`). If multiple threads execute `process_job` or `add_job` concurrently, they can corrupt the dictionaries or read inconsistent state.

The fix requires introducing a `threading.Lock` to ensure that only one thread can modify or read the critical sections (the internal state of the queue) at any given time.

### Fixed Implementation

```python
import threading

class JobQueue:
    def __init__(self):
        self.jobs = {}
        self.results = {}
        # Initialize the lock to protect shared resources
        self.lock = threading.Lock()

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

    def process_job(self, job_id, processor):
        # Step 1: Check for job and retrieve data safely
        data = None
        with self.lock:
            if job_id not in self.jobs:
                return False
            # Retrieve the data while holding the lock
            data = self.jobs[job_id]
            # IMPORTANT: Remove the job from the queue immediately to prevent
            # other threads from processing it simultaneously.
            del self.jobs[job_id]

        # Step 2: Execute the external processor (outside the lock)
        # This prevents blocking the entire queue while a long computation runs.
        result = processor(data)

        # Step 3: Store the result safely
        with self.lock:
            self.results[job_id] = result
        
        return True

    def get_result(self, job_id):
        # Acquire lock before reading self.results
        with self.lock:
            return self.results.get(job_id)

# --- Example Usage (Demonstration) ---

def dummy_processor(data):
    import time
    time.sleep(0.01) # Simulate work
    return f"Processed: {data}"

if __name__ == '__main__':
    queue = JobQueue()
    
    # Add jobs
    job_id_1 = queue.add_job(1, "Task A")
    job_id_2 = queue.add_job(2, "Task B")
    
    # Setup threads
    def worker(job_id, processor):
        success = queue.process_job(job_id, processor)
        if success:
            print(f"Thread finished processing job {job_id}")

    t1 = threading.Thread(target=worker, args=(job_id_1, dummy_processor))
    t2 = threading.Thread(target=worker, args=(job_id_2, dummy_processor))

    # Start threads
    t1.start()
    t2.start()

    # Wait for threads to complete
    t1.join()
    t2.join()

    # Check results
    print("\n--- Results ---")
    print(f"Result for Job 1: {queue.get_result(job_id_1)}")
    print(f"Result for Job 2: {queue.get_result(job_id_2)}")
    print(f"Jobs remaining in queue: {queue.jobs}") # Should be empty
```

### Explanation of the Fix

1.  **`self.lock = threading.Lock()`:** A lock object is initialized in the constructor. This object acts as a gatekeeper for the shared data.
2.  **`with self.lock:`:** This is the crucial fix. By using the `with` statement, we ensure that:
    *   The lock is acquired before the code block runs (the thread waits if the lock is held by another thread).
    *   The lock is automatically released when the code block finishes, even if an exception occurs.
3.  **Critical Section Protection:**
    *   In `add_job` and `get_result`, the lock protects simple dictionary read/writes.
    *   In `process_job`, we implemented a pattern to minimize lock holding time:
        *   **Lock 1 (Acquire/Retrieve/Delete):** We acquire the lock only long enough to safely check for the job, retrieve the data, and immediately remove the job from `self.jobs`. This ensures the job cannot be processed twice.
        *   **External Work (No Lock):** The potentially long-running `processor(data)` function executes *outside* the lock, allowing other threads to add new jobs or retrieve results while the computation is happening.
        *   **Lock 2 (Store Result):** We acquire the lock again to safely write the final `result` into `self.results`.

This approach solves the race condition while maintaining good thread performance by avoiding unnecessary blocking during computation.