Can we say "put the lid on the box" and "take the lid off the box" when one side of the lid is joined to the box?

Question

We can say "slide the lid open / closed" as shown in the above picture

Or

We can say "snap/click the lid open / closed" as shown in the above picture

But what about this one

Note that one side of the lid is joined to the box so we can only move the lid freely into "on-off" position. And, I am not sure we can "take it off" and "put it on".

Can we say "move the lid open / closed" in this case?

Answer 1

That hinged part is the lid. I'd understand "Take the lid off". (Even though it could mean "cut it off with sissors")

However, the simple expression is "Open the box"/"Close the box". No need to mention lids at all.

You could say "lift the lid" if using the word lid is important.

Answer 2

Shut the lid. Open the lid. Flip it open, close the lid.