why is the determiner so important here? Why can't it be " you don't need A lamp."?
You don't need lamps: bạn không cần đèn (no classifier)
You don't need the lamp: bạn không cần cái đèn
You don't need a lamp: bạn không một cái đèn
First and last one would mean almost the same (I'm not even sure the last one makes sense in Vietnamese).
When you use the classifier without "một", it means "the".
In this case we can guess they are speaking about one specific lamp. For example I take the lamp from your room, and when you ask me, I tell you that you don't need it.