Certainly! Let's create a test case generator for the given problem "Palindrome".

The goal is to generate random test cases that adhere to the problem constraints and format. 

Here is the implementation of the test case generator:

```python
import random
import string

def generate_random_string(length):
    return ''.join(random.choices(string.ascii_lowercase, k=length))

def tcgen():
    # Number of strings, 1 ≤ N ≤ 1000
    N = random.randint(1, 1000)
    
    # Length of each string, 1 ≤ L ≤ 30
    L = random.randint(1, 30)
    
    # Generate N strings of length L
    strings = [generate_random_string(L) for _ in range(N)]
    
    return N, L, strings

# Example usage of the generator
N, L, strings = tcgen()
print(N)
print(L)
for s in strings:
    print(s)
```

This code will create a valid random test case for the problem statement. It:

1. Generates a random integer `N` between 1 and 1000.
2. Generates a random integer `L` between 1 and 30.
3. Creates `N` strings each of length `L` consisting of lowercase English letters.

You can run this script to generate random test cases and use them to test the solution for the problem "Palindrome".