Certainly! Below is the test case generator for the provided problem statement:

```python
import random
import string

def tcgen():
    # Generate random length for the string S within the constraints
    N = random.randint(1, 500000)
    
    # Generate the string S consisting of lowercase English letters
    S = ''.join(random.choices(string.ascii_lowercase, k=N))
    
    # Generate random number of queries within the constraints
    Q = random.randint(1, 20000)
    
    queries = []
    type2_present = False
    
    for _ in range(Q):
        query_type = random.choice([1, 2])
        
        if query_type == 1:
            # Type 1 query: change the i_q-th character of S to c_q
            i_q = random.randint(1, N)
            c_q = random.choice(string.ascii_lowercase)
            queries.append(f"1 {i_q} {c_q}")
        else:
            # Type 2 query: answer the number of different characters in the substring S[l_q:r_q]
            l_q = random.randint(1, N)
            r_q = random.randint(l_q, N)
            queries.append(f"2 {l_q} {r_q}")
            type2_present = True
    
    # Ensure there is at least one query of type 2
    if not type2_present:
        l_q = random.randint(1, N)
        r_q = random.randint(l_q, N)
        queries.append(f"2 {l_q} {r_q}")
    
    return N, S, Q, queries

# Example usage:
N, S, Q, queries = tcgen()
print(N)
print(S)
print(Q)
for query in queries:
    print(query)
```

### Explanation:
1. **N Generation**: Randomly generate the length of the string \( N \) within the constraint \( 1 \leq N \leq 500000 \).
2. **String S Generation**: Create a string \( S \) of length \( N \) consisting of random lowercase English letters.
3. **Q Generation**: Randomly generate the number of queries \( Q \) within the constraint \( 1 \leq Q \leq 20000 \).
4. **Queries Generation**: Generate \( Q \) queries:
   - **Type 1 Query**: Randomly choose an index \( i_q \) within the range \( 1 \leq i_q \leq N \) and a lowercase letter \( c_q \).
   - **Type 2 Query**: Randomly choose \( l_q \) and \( r_q \) such that \( 1 \leq l_q \leq r_q \leq N \).
5. **Guarantee Type 2 Query**: Ensure at least one query of type 2 is present in the generated queries.

The function returns \( N \), \( S \), \( Q \), and the list of queries.