Certainly! Here's a test case generator for the problem statement you provided. The generator will produce random strings `s` and `t` consisting of lowercase English letters, which can be used to test your solution:

```python
import random
import string

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

# Example usage:
s, t = tcgen()
print("s:", s)
print("t:", t)
```

### Explanation:

1. **Random Lengths for `s` and `t`**:
   - `s_length`: Random integer between 1 and 100,000.
   - `t_length`: Random integer between 1 and 100,000.

2. **Random Strings Generation**:
   - `s`: Randomly chosen lowercase letters of length `s_length`.
   - `t`: Randomly chosen lowercase letters of length `t_length`.

3. **Output**:
   - The function returns two strings `s` and `t`.

You can use the generated test cases to validate the correctness and performance of your solution for the given problem statement.