```python
def lay_conveyor(floor: list, row: int, col: int, length: int) -> list:
    if length <= 0:
        raise ValueError("Length must be greater than zero")
    
    if row < 0 or row >= len(floor):
        raise ValueError("Row out of bounds")
    
    if col < 0 or col + length > len(floor[row]):
        raise ValueError("Conveyor run would leave the plan")
    
    new_floor = [row[:] for row in floor]
    for i in range(length):
        if new_floor[row][col + i] != ".":
            raise ValueError("Cell not open")
        new_floor[row][col + i] = "="
    
    return new_floor
```