Certainly! Here is the test case generator for the problem "Lunch":

```python
import random

def tcgen():
    # Generate three unique calorie values between 1 and 5000
    a = random.randint(1, 5000)
    b = random.randint(1, 5000)
    c = random.randint(1, 5000)
    
    # Ensure all three values are unique
    while b == a:
        b = random.randint(1, 5000)
    while c == a or c == b:
        c = random.randint(1, 5000)
    
    return a, b, c

# Example of using the generator
a, b, c = tcgen()
print(f"{a} {b} {c}")
```

This code generates three unique integers \(a\), \(b\), and \(c\) between 1 and 5000, ensuring they are all different, which satisfies the problem constraints.

You can use this function to generate random test cases. Here is an example of how to use the generator and derive the output based on the problem statement:

```python
def determine_menu_to_give_up(a, b, c):
    # Find the maximum value
    max_calories = max(a, b, c)
    
    # Determine which menu to give up
    if max_calories == a:
        return "A"
    if max_calories == b:
        return "B"
    return "C"

# Using the generated test case
a, b, c = tcgen()
print(f"Input: {a} {b} {c}")
print(f"Output: {determine_menu_to_give_up(a, b, c)}")
```

The function `determine_menu_to_give_up` calculates which menu Kawabayashi-kun should give up by finding the maximum calorie count and returning the corresponding menu label.