```python
def lay_conveyor(floor: list, row: int, col: int, length: int) -> list:
    if not floor or row < 0 or row >= len(floor) or col < 0 or col + length > len(floor[0]):
        raise ValueError("Run would leave the plan.")
    
    for i in range(length):
        if floor[row][col + i] != ".":
            raise ValueError(f"Cell at ({row}, {col + i}) is not open.")
    
    new_floor = [row[:] for row in floor]
    for i in range(length):
        new_floor[row][col + i] = "="

    return new_floor
```