This concurrency bug arises because the operations on the shared state (`self.jobs` and `self.results`) are not atomic. When multiple threads call `process_job` simultaneously, they can interrupt each other between checking for the job's existence, retrieving the data, writing the result, and deleting the job.

To fix this, we introduce a `threading.Lock` and use it to protect all critical sections where shared state is read or modified.

### 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 shared state
        with self._lock:
            self.jobs[job_id] = data
        return job_id

    def process_job(self, job_id, processor):
        result = None
        success = False
        
        # Acquire lock to ensure atomic read/write/delete sequence
        with self._lock:
            if job_id not in self.jobs:
                return False

            # 1. Get data and remove job immediately (critical step)
            data = self.jobs[job_id]
            del self.jobs[job_id]
            
            # 2. Process the job (NOTE: We release the lock here for performance 
            # if the processor function is long-running. If the processor must 
            # access other shared state, the lock must be held.)
            # For this simple example, we'll run the processing outside the lock 
            # to prevent holding the lock during potentially long CPU work.
            pass # Data is retrieved, job is removed.
        
        # Run the CPU-intensive task outside the lock
        try:
            result = processor(data)
            success = True
        except Exception as e:
            print(f"Error processing job {job_id}: {e}")
            # Optionally, handle failed jobs here
            return False


        # Acquire lock again to safely write the result
        with self._lock:
            if success:
                self.results[job_id] = result
            # If processing failed, we might choose to leave the job out of results
            
        return success

    def get_result(self, job_id):
        # Acquire lock even for reading to ensure we don't read results 
        # while another thread is concurrently deleting or updating the dictionary.
        with self._lock:
            return self.results.get(job_id)

# --- Example Usage Verification ---

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

if __name__ == '__main__':
    queue = JobQueue()
    
    # Add jobs
    job_id1 = queue.add_job(1, "Task A")
    job_id2 = queue.add_job(2, "Task B")
    
    threads = []
    
    def worker(job_id):
        queue.process_job(job_id, mock_processor)

    # Create multiple threads trying to process the jobs
    t1 = threading.Thread(target=worker, args=(job_id1,))
    t2 = threading.Thread(target=worker, args=(job_id2,))
    
    threads.append(t1)
    threads.append(t2)

    t1.start()
    t2.start()

    for t in threads:
        t.join()

    print(f"Job 1 result: {queue.get_result(job_id1)}")
    print(f"Job 2 result: {queue.get_result(job_id2)}")
    
    # Verify that no jobs are left in the queue
    with queue._lock:
        print(f"Jobs remaining in queue: {queue.jobs}")
```

### Explanation of the Fixes

1.  **`self._lock = threading.Lock()`:** A lock object is initialized in `__init__`. This object acts as a gatekeeper.
2.  **`with self._lock:`:** Using the `with` statement is the standard Python pattern for managing locks. It ensures that:
    *   `self._lock.acquire()` is called before the code block runs.
    *   `self._lock.release()` is called when the code block exits, even if an exception occurs.
3.  **`add_job` and `get_result`:** These methods now use the lock to ensure that dictionary modifications or reads are synchronized.
4.  **`process_job` (Critical Fix):**
    *   The most critical part is the sequence: Check $\rightarrow$ Retrieve $\rightarrow$ Delete. This sequence *must* be atomic.
    *   In the fixed version, we acquire the lock, check for the job, retrieve the data, and immediately **delete** the job from `self.jobs` *while holding the lock*. This prevents any other thread from picking up the same job.
    *   We then **release the lock** before calling `processor(data)`. This is crucial for performance; if the processing takes 5 seconds, we don't want to block all other threads for 5 seconds.
    *   Finally, we acquire the lock *again* to safely write the `result` into `self.results`.

By using locks, we guarantee that only one thread can modify or inspect the shared state (`self.jobs` and `self.results`) at any given time, eliminating the race condition.