The correct option is C lest
Here, 'lest' as a conjunction is correct because it is used in order to prevent something from happening. Here, the teacher wrote the names 'lest' she should forget.
'Because' is used to imply for the reason that. Example: He studied because he wanted to succeed.
'In order to', as an idiom, is used with the purpose or intention of doing or achieving something.
'So as not to' implies 'in order not to'.