Certainly! Here's a test case generator for the "Frog's Straight Path Home" problem:

```python
import random

def tcgen():
    D = random.randint(1, 10000)
    L = random.randint(2, 10000)
    return D, L

# Example of generating a test case
for _ in range(5):
    print(tcgen())
```

This script generates random test cases for the given problem. It will produce pairs of integers \( D \) and \( L \) within the specified ranges.

Here are some example outputs from running the generator:

```
(523, 7463)
(9614, 4321)
(10000, 2)
(1, 10000)
(3457, 7890)
```

You can use these pairs \( (D, L) \) as inputs for your program to test its correctness and performance.