Certainly! Below is the test case generator for the provided problem statement involving a triangular grid with lamps.

```python
import random

def tcgen():
    N = random.randint(1, 10**4)
    
    lamps = set()
    while len(lamps) < N:
        x = random.randint(-10**17, 10**17)
        y = random.randint(-10**17, 10**17)
        lamps.add((x, y))
    
    lamps_list = list(lamps)
    
    return N, lamps_list

def format_input(N, lamps_list):
    formatted_input = f"{N}\n"
    for x, y in lamps_list:
        formatted_input += f"{x} {y}\n"
    return formatted_input

# Example Usage
N, lamps_list = tcgen()
input_data = format_input(N, lamps_list)
print(input_data)
```

This script generates a test case for the problem. It creates a random number of lamps `N` within the constraints and ensures that the coordinates of the lamps are unique. It also formats the input to match the expected standard input format for the problem.

### Explanation:
1. **Generating `N`**: Randomly choose the number of lamps `N` between 1 and 10,000.
2. **Generating Unique Lamp Coordinates**: Use a set to store unique lamp coordinates. Randomly generate `x` and `y` coordinates in the range \([-10^{17}, 10^{17}]\) until we have `N` unique lamps.
3. **Formatting the Input**: Convert the set of lamps to a list and format it into the required input format.

The `format_input` function is used to convert the generated test case into the format specified in the problem statement, making it easy to pass the input to your solution for testing.