The correct option is A has not been started by the teacher.
The correct answer is ‘has not been started by the teacher’. In passive voice, the receiver of the action appears first and since the receiver is singular, ‘the lecture’, the singular form of the helping verb, ‘has’ is used. It is followed by the negative word ‘not’, the ‘be’ verb form ‘been’, the past participle form of the main verb ‘start’ which is ‘started’, the preposition ‘by’ and the doer of the action, ‘the teacher.’