Certainly! Below is a test case generator for the "Problem A: Lunch" problem. This generator will create random test cases adhering to the constraints provided.

```python
import random

def tcgen():
    # Generate three distinct integers between 1 and 5000
    a, b, c = random.sample(range(1, 5001), 3)  # random.sample ensures distinct values
    
    return a, b, c

# Example of using the test case generator
for _ in range(5):  # Generate 5 test cases for demonstration
    a, b, c = tcgen()
    print(f"{a} {b} {c}")
```

You can use this function to generate test cases for the problem. Here's how it works:

- `random.sample(range(1, 5001), 3)` generates three distinct integers between 1 and 5000.
- The function returns a tuple containing these three integers.

The generated test cases will always meet the problem's constraints:
- All three integers are distinct.
- Each integer is between 1 and 5000, inclusive.

You can run the provided example loop to see a few sample test cases generated by this function.