```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("Invalid run dimensions")
    
    new_floor = [row[:] for row in floor]
    for i in range(length):
        if new_floor[row][col + i] != '.':
            raise ValueError("Run covers a non-open cell")
        new_floor[row][col + i] = '='
    
    return new_floor
```