Certainly! Here is a test case generator for the given problem statement:

```python
import random
import string

def tcgen():
    # Generate a random length for string s and t within the given constraints
    len_s = random.randint(1, 10**5)
    len_t = random.randint(1, 10**5)
    
    # Generate random strings s and t of the specified lengths
    s = ''.join(random.choices(string.ascii_lowercase, k=len_s))
    t = ''.join(random.choices(string.ascii_lowercase, k=len_t))
    
    return s, t

# Generate a test case
s, t = tcgen()
print(s)
print(t)
```

This generator follows the constraints of the problem:
- Length of `s` and `t` are between 1 and 100,000.
- Both strings `s` and `t` consist of lowercase English letters.

You can run this generator multiple times to create different test cases for the problem.