Sure, here is a test case generator for the given problem statement "Escape of Lappin the Phantom Thief":

```python
import random

def tcgen():
    # Generate n and m within the specified range
    n = random.randint(1, 5 * 10**4)
    m = random.randint(1, 5 * 10**4)
    
    # Generate k which is min(10^5, n * m)
    k = random.randint(1, min(10**5, n * m))

    # Generate k unique coordinates for the robots
    robots = set()
    while len(robots) < k:
        x = random.randint(0, n - 1)
        y = random.randint(0, m - 1)
        robots.add((x, y))
    
    # Convert the set of robots to a list of coordinates
    robots = list(robots)
    
    # Preparing the input in the required format
    input_data = f"{n} {m} {k}\n"
    for robot in robots:
        input_data += f"{robot[0]} {robot[1]}\n"
    
    # Output the input data as a string
    return input_data

# Example usage to generate a test case
print(tcgen())
```

This function generates a test case for the "Escape of Lappin the Phantom Thief" problem by:
1. Randomly selecting dimensions `n` and `m` for the grid within the specified range.
2. Randomly determining the number of robots `k` considering the constraints.
3. Generating `k` unique coordinates for the robots.
4. Formatting the generated data as required by the problem statement.

You can call this function to generate different test cases. The function ensures that robot coordinates are unique and fit within the bounds of the grid.